GENEVA—The U.S. and five other world powers struck a historic accord with Iran on Sunday, agreeing to ease part of an economic stranglehold in exchange for steps to cap Tehran's nuclear program and ensure the Islamist government doesn't rush to develop atomic weapons.

The agreement calls for Iran to stop its production of near-weapons-grade nuclear fuel—which is uranium enriched to 20% purity—and for the removal of Tehran's stockpile of the fissile material, which is estimated to be nearly enough to produce one nuclear bomb.

Iran, in return, will gain relief from Western economic sanctions that U.S. officials believe will provide between $6 billion and $7 billion in badly needed foreign exchange for Tehran over the next half-year.

The agreement reached in Geneva is an interim deal for about six months that will allow international powers to try to strike a permanent pact, an effort that experts said would be the true test of Iran's new government, headed by revitalization-minded President Hasan Rouhani.

President Barack Obama called the agreement "an important first step toward a comprehensive solution" of the Iranian nuclear dilemma and credited his administration's push for diplomacy and its adoption of stern economic sanctions for "a new path toward a world that is more secure."

"The first step that we have taken today marks the most significant and tangible progress that we have made with Iran since I took office," he said, adding that the next steps "won't be easy."

While U.S. officials argued that the deal will roll back Iran's nuclear program, critics of the diplomacy are likely to seize on key Western concessions, including a signal that Washington ultimately will agree to accept Iran's enrichment of uranium and would leave open for now the future of Tehran's plutonium-producing reactor in Arak.

Israel, which has been a strong opponent of U.S. efforts to negotiate with Iran, was quick to criticize the development. "This is a bad agreement. It gives Iran exactly what it wants: both substantial easing of sanctions and preservation of the most substantial parts of its nuclear program,'' said a statement from Prime Minister Benjamin Netanyahu's office on Sunday.

U.S. Secretary of State John Kerry tried Sunday to rally support for the deal in the face of lukewarm reaction from U.S. congressional allies and hostility from critics. "We make sure that these sanctions don't get lifted in a way that reduces the pressure on Iran," Mr. Kerry said on CNN's "State of the Nation." "The Iranian nuclear program is actually set backward and is actually locked into place in critical places."

The first test will be whether Congress presses ahead with a new round of broader sanctions, despite the administration's entreaties. The U.S. House of Representatives has already voted for such an effort. U.S. Senate Majority Leader Harry Reid (D., Nev.) last week said he was prepared to hold a Senate vote when Congress returns from its Thanksgiving recess, citing skepticism about the trustworthiness of Iran. A spokesman didn't reply to questions about whether the new diplomatic deal would change those plans.

U.S. lawmakers took to the airwaves Sunday morning to question whether the deal would work, with some suggesting that the Obama administration had made a strategic miscalculation. "Instead of easing them, now is the time to tighten those sanctions," said Sen. Saxby Chambliss (R., Ga.) on ABC's "Face the Nation." He predicted that "you're going to see a strong movement in the United States Senate to move ahead to tighten sanctions," even if the new deal meant that legislation would have to be worded in a way that accounted for the six-month deal. He said the Obama administration can proceed with the deal without Congress's approval.

Sen. Bob Corker (R., Tenn.), the top Republican on the Senate Foreign Relations Committee," expressed skepticism about the deal on "Fox News Sunday, saying "I think we all greet it with skepticism." He said that the arrangement suggested that Iranian officials "view this administration as weak," and "see this as their window of opportunity to negotiate with an administration that has shown that it really doesn't have a lot of the intestinal fortitude that other administrations have had."

In a sign of the tension with Congress, the Obama administration's Democratic allies offered only tepid support for the deal. Many Democrats left open the possibility that Congress should still tighten sanctions. In general, Congress believes that the current sanctions are what brought Iran to the negotiating table in the first place, and lawmakers recall how the Obama administration fought off the last round of sanctions in 2011.

"I think this is a marginal improvement," said Rep. Steny Hoyer (D., Md.), the House minority whip, on CBS's "Face the Nation." Mr. Hoyer said that he believed the Senate should still move ahead with a vote on tougher sanctions on Iran that mirrored legislation already passed in the House, but that the U.S. should hold off implementing them for six months so that they could serve as a warning to Iran and an incentive to reach a final deal.

The first-stage deal also takes no steps to force Iran to ship out or destroy the roughly 19,000 centrifuge machines it has amassed to produce nuclear fuel.

U.S. lawmakers and key American allies have said Iran will abandon its nuclear program only if international pressure is increased.

"This deal appears to provide the world's leading sponsor of terrorism with billions of dollars in exchange for cosmetic concessions," said Sen. Mark Kirk (R., Ill.) a leading proponents of increasing sanctions on Iran during the talks.

The deal was completed during three exhaustive negotiating sessions over the past month in Geneva involving Iran and the five permanent members of the United Nations Security Council and Germany, a diplomatic bloc called the P5+1.

Mr. Kerry and the foreign ministers of the other members of the P5+1 states traveled to the Swiss lakeside city over the weekend to push through the final agreement—their second such visit in two weeks.

American and Iranian officials called the deal a potential turning point in Tehran's relations with the international community and an important "first step" in ending the decadelong standoff over Iran's nuclear program.

"The agreement creates the time and space for a comprehensive solution," said Catherine Ashton, the European Union's foreign policy chief, who leads the P5+1.

U.S. and European officials said the six months that the interim agreement covers will be used to forge a broader accord that permanently ends the threat posed by Tehran's nuclear work. Iranian officials stressed this week that the nuclear program only had civilian uses.

France played a major role in the negotiations, with Foreign Minister Laurent Fabius insisting publicly during a previous round of talks two weeks ago that a draft agreement being discussed wasn't strong enough. In a statement early Sunday, Mr. Fabius acknowledged that the discussions were long and difficult but said the Geneva accord "amounts to a first major step" to resolve the nuclear dispute.

Mr. Fabius said the deal includes strict oversight of Iran's commitments and that "we will have to be vigilant on their implementation."

Speaking to reporters after the deal was signed, U.K. Foreign Secretary William Hague confirmed Iran would win sanctions relief under the accord affecting its gold and precious metals trade, its petrochemicals sector and including the unfreezing of assets by U.S. officials.

American, European and Iranian officials described on Saturday a testy three days of talks that were needed to forge the final deal. The question of what to do with Iran's heavy water reactor nearing completion in the city of Arak nearly killed an agreement in the later stages of the diplomacy, said these officials.

France was pushing for a complete dismantling of the reactor on the grounds that there exists no nonmilitary rational for building the facility. The U.S. government shared this position.

Under the deal, Iran agreed to significantly increase inspections of Arak by the U.N.'s nuclear watchdog, the International Atomic Energy Agency and agree not to start the facility or lead it with nuclear fuel.

Iran also agreed to cap its enrichment of uranium to levels only usable as fuel for a reactor, which is a purity of 3.5% to 5%.

Iran committed to maintaining its total stockpile of the low-enriched nuclear fuel at its current level, which is around six tons, during the six-month period.

Iran and the P5+1 also forged a compromise over the issue that over the past few days looked as though it could squelch a deal—Tehran's demand that the international community accept its "right" to continue producing nuclear fuel domestically.

Tehran cites the U.N.'s nuclear Nonproliferation Treaty as affording every signatory that legal right to enrich uranium, provided it is used for civilian purposes. Successive U.S. administrations have denied this right exists and have supported multiple U.N. Security Council resolutions requiring Tehran to suspend its enrichment activities.

In a compromise, the P5+1 agreed to a text that says Iran will enjoy all the rights of treaty signatories, provided Iran satisfies all of the IAEA's questions about the alleged military dimensions of Iran's program. But the U.S. and its partners won't be forced to formally accept that Iran will be allowed to enrich.

Still, the compromise is seen as a victory for Iran, which has campaigned for a decade on this issue. U.S. officials on Saturday acknowledged that Iran will likely be allowed to maintain some enrichment capacity on its soil as part of a final deal.

"We're interested in exploring how Iran might end up with a limited and tightly controlled facility to enrich," said a senior U.S. official.

Iranian Foreign Minister Javad Zarif touted the deal as vindicating Tehran's position. "Iran enjoys that right and its important to recognize that right. This recognition is there," Mr. Zarif told reporters. "We believe that to be our right."

U.S. officials said the agreement will provide sanctions relief of between $6 billion to $7 billion over the next six months, a number far below estimates made by critics of the agreement, including the government of Israel. The Obama administration also stressed that any easing of the sanctions could be quickly reversed if Iran is found not complying with the agreement.

U.S. officials said the P5+1 immediately will begin helping Iran repatriate about $4.2 billion in oil revenues that it hasn't been able to access overseas as a result of the sanctions. Iran is estimated to have $50 billion in these revenues overseas, which its government has been unable to access. The funds will be returned to Iran in monthly installments of $600 million.

The agreement also calls for the U.S. and European Union to ease the ban on Iran's trade in petrochemicals, precious metals, automobiles and airplane spare parts. U.S. and European officials said they didn't believe that such commerce could derive more than a few billion dollars in revenues for Tehran over the next six months. But they said some of the trade—such as access to airline parts—is critical to Iran, which has increasingly found its jetliners grounded because of safety concerns.

U.S. officials stressed that the sanctions relief would still be dwarfed by the revenue Iran is still losing because of the pervasive sanctions that remain in place.

These diplomats estimated that Iran still is likely to lose around $25 billion over the six months to the U.S. and European embargo against oil purchases. They also believed Tehran will continue to find itself unable to repatriate the earnings from the oil its does sell in Asia and the Middle East, because of sanctions. One official said Iran was likely to find itself unable to access another $14 billion to $16 billion in oil earnings over the next six months.

"The pressure of the sanctions will continue to grow," said a second American official involved in the Geneva talks.

U.S. and Iranian officials both said the agreement had potentially profound implications for global security and stability in the Middle East.

Before Mr. Rouhani's August inauguration, diplomatic engagement between Washington and Tehran was largely frozen, as it had been since the 1979 Islamic revolution. Over the past three months, however, Mr. Obama has held a phone conversation with President Rouhani, and Secretary of State John Kerry and Mr. Zarif have held hours of negotiations in Geneva.

"I think this is potentially a significant moment," Mr. Kerry said following the negotiations. "But I'm not going to say this is an end unto itself."

Mr. Rouhani tweeted after the agreement was signed Sunday: "We are confident that the agreement between Iran and the West will have a positive impact on other regional and global issues."

—Joshua Mitnick in Tel Aviv contributed to this article.