World powers and Iran agreed Monday to extend negotiations over Iran’s nuclear program for up to an additional seven months after they failed in a last-minute push to conclude a broad deal by a midnight deadline.

Negotiators framed the extension as a chance to build on momentum achieved during a year of talks and said an interim agreement will continue to restrain any attempt by Iran to develop a nuclear weapon.

But the failure to reach a permanent accord also opened the door to a renewed effort by congressional Republicans — who will assume control of the Senate in January — to pressure Iran with stepped-up economic sanctions, measures that the Obama administration has long argued could scuttle the possibility of a permanent deal.

During a news conference here, Secretary of State John F. Kerry vowed to brief lawmakers fully, saying he believed “we have earned the benefit of the doubt.”

“Real and substantial progress” was made, particularly during the past several days of near round-the-clock talks here to close remaining gaps between the two sides, Kerry said. He acknowledged that “significant points of disagreement” remain.

“These talks are not going to get any easier just because we extend them,” he said. “They’re tough.”

The extension is the second since the interim agreement was reached a year ago. That deal limits the number of centrifuges Iran can operate to enrich uranium — essentially preventing any new ones from coming on line — and restricts the level of enrichment to far below levels that would be needed to develop a nuclear weapon. Iran gave up its stockpile of uranium enriched to high levels and agreed to enhanced international inspections to ensure compliance. The interim deal also freed some frozen Iranian assets and provided limited relief from sanctions.

The new extension keeps those terms in place. It imposes no new restraints on Iran’s nuclear program and gives Iran no additional relief from sanctions. It will continue to thaw a relatively modest amount of Iran’s frozen assets, which British Foreign Secretary Philip Hammond estimated at about $700 million a month.

Kerry declined to specify the remaining gaps in the talks, which are said to center on the number of centrifuges Iran is allowed to permanently operate and the level of permitted enrichment, as well as on new levels of inspection, especially on military aspects of Iranian technology.

Iran has long insisted that it has no intention of developing a nuclear weapon but that it has the right to a nuclear program for peaceful purposes such as energy and medical research.

Although the extension lasts through June, Kerry and other leaders here said they anticipate that the framework of a political accord will be established well before that.

“At the end of four months, if we have not agreed on major elements at that point in time and there is no clear path forward, we can revisit how we then want to proceed,” Kerry said.

In a televised address, Iranian President Hassan Rouhani agreed that gaps had been closed, saying there is still “some distance” to a final agreement. But he predicted that more negotiations “will lead to a deal, sooner or later.”

Reaction in Congress was mixed, with Democrats largely agreeing that continued talks were warranted. Some Republicans were grudgingly supportive, while warning that Congress must approve any final agreement.

“I would rather the administration continue to negotiate than agree to a bad deal,” said Sen. Bob Corker (Tenn.), the ranking Republican on the Foreign Relations Committee. “Congress must have the opportunity to weigh in before implementation of any final agreement and begin preparing alternatives, including tougher sanctions, should negotiations fail.”

Others, however, said the time has come to step up pressure on Iran.

While not directly mentioning new sanctions, House Speaker John A. Boehner (R-Ohio) said: “At this point, all an extension does is leave open the possibility this administration will make additional concessions. . . . Instead of giving Iran more flexibility, we should be holding this regime accountable for the threat it poses to the region and our allies.”

House Intelligence Committee Chairman Mike Rogers (R-Mich.) said the negotiations “have done little to advance the security of the United States and our allies, but they have benefited Iran,” which has been allowed to continue enrichment and won back some of its sanctions-frozen assets.

“While the White House longs for a deal, Iran strengthens its hand,” Rogers said. “It is time for the administration to reconsider its entire approach to Iran.”

Sen. John McCain (R-Ariz.), slated to become chairman of the Armed Services Committee in January, and Republican Sens. Lindsey O. Graham (S.C.) and Kelly Ayotte (N.H.) said in a joint statement that “this latest extension of talks should be coupled with increased sanctions” and a requirement that Congress approve any final deal.

In meetings with senior administration officials over the past two weeks, congressional leaders have said that, at a minimum, any extension must have a firm timeline and not include additional money for Iran or any change in the restrictions.

Kerry said Iran has held up its end of the interim agreement, a conclusion supported by a new update on Iran’s implementation of the interim accord by the International Atomic Energy Agency.

“When properly briefed,” Kerry said of lawmakers, “I hope they will come to see the wisdom of leaving us the equilibrium for a few months to be able to proceed, without sending messages that might be misinterpreted and cause miscalculation. . . . I look forward to those discussions when I get back.”

Israeli Prime Minister Benjamin Netanyahu, who has warned that Iran would take advantage of what he sees as administration eagerness for an accord, expressed relief that the interim agreement would remain in place.

“The deal that Iran was pushing for was terrible,” Netanyahu told the BBC, and “would have left Iran with the ability to enrich uranium for an atom bomb while removing the sanctions.”

Israel, Netanyahu said, “is watching very carefully what is happening here, and Israel always — always — reserves the right to defend itself.”

Other world powers that are part of the negotiations — Britain, France, China, Russia and Germany and the European Union — framed the extension as a chance to build momentum achieved in the most recent rounds and to concentrate on working out specific ways to implement and enforce a deal.

“Substantial progress was made,” Russian Foreign Minister Sergei Lavrov told the Tass news agency.

Although he declined to supply details of apparent strides made in the latest round, Kerry enumerated what he said had been achieved.

“The nuclear program in Iran as we negotiate is frozen,” and Iran’s stockpile of uranium enriched to 20 percent “has been reduced to zero,” he said. “Inspectors are in the facilities. . . . There’s no change in the level of centrifuges.”

“We would be fools to walk away from a situation where the breakout time,” the amount of time it would take Iran to produce a nuclear weapon, “has been expanded rather than narrowed, and where the world is safer because this program is in place,” Kerry said.

DeYoung reported from Washington. Brian Murphy and Ed O’Keefe in Washington and Ruth Eglash in Jerusalem contributed to this report.