WASHINGTON � The White House relented on Tuesday and said President Obama would sign a compromise bill giving Congress a voice on the proposed nuclear accord with Iran as the Senate Foreign Relations Committee, in rare unanimous agreement, moved the legislation to the full Senate for a vote.

An unusual alliance of Republican opponents of the nuclear deal and some of Mr. Obama�s strongest Democratic supporters demanded a congressional role as international negotiators work to turn this month�s nuclear framework into a final deal by June 30. White House officials insisted they extracted crucial last-minute concessions. Republicans � and many Democrats � said the president simply got overrun.

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�We�re involved here. We have to be involved here,� said Senator Benjamin L. Cardin of Maryland, the committee�s ranking Democrat, who served as a bridge between the White House and Republicans as they negotiated changes in the days before the committee�s vote on Tuesday. �Only Congress can change or permanently modify the sanctions regime.�

The essence of the legislation is that Congress will have a chance to vote on whatever deal emerges with Iran � if one is reached by June 30 � but in a way that would be extremely difficult for Mr. Obama to lose, allowing Secretary of State John Kerry to tell his Iranian counterpart that the risk that an agreement would be upended on Capitol Hill is limited.

As Congress considers any accord on a very short timetable, it would essentially be able to vote on an eventual end to sanctions, and then later take up the issue depending on whether Iran has met its own obligations. But if it rejected the agreement, Mr. Obama could veto that legislation � and it would take only 34 senators to sustain the veto, meaning that Mr. Obama could lose upward of a dozen Democratic senators and still prevail.

The bill would require that the administration send the text of a final accord, along with classified material, to Congress as soon as it is completed. It also halts any lifting of sanctions pending a 30-day congressional review, and culminates in a possible vote to allow or forbid the lifting of congressionally imposed sanctions in exchange for the dismantling of much of Iran�s nuclear infrastructure. It passed 19 to 0.

Why Mr. Obama gave in after fierce opposition was the last real dispute of what became a rout. Josh Earnest, the White House spokesman, said Mr. Obama was not �particularly thrilled� with the bill, but had decided that a new proposal put together by the top Republican and Democrat on the Senate Foreign Relations Committee made enough changes to make it acceptable.

�We�ve gone from a piece of legislation that the president would veto to a piece of legislation that�s undergone substantial revision such that it�s now in the form of a compromise that the president would be willing to sign,� Mr. Earnest said. �That would certainly be an improvement.�

Senator Bob Corker, Republican of Tennessee and the committee�s chairman, had a far different interpretation. As late as 11:30 a.m., in a classified briefing at the Capitol, Mr. Kerry was urging senators to oppose the bill. The �change occurred when they saw how many senators were going to vote for this, and only when that occurred,� Mr. Corker said.

Mr. Cardin said that the �fundamental provisions� of the legislation had not changed.

But the compromise between him and Mr. Corker did shorten a review period of a final Iran nuclear deal and soften language that would make the lifting of sanctions dependent on Iran�s ending support for terrorism.

The agreement almost certainly means Congress will muscle its way into nuclear negotiations that Mr. Obama sees as a legacy-defining foreign policy achievement.

The Senate is expected to vote on the legislation this month, and House Republican leaders have promised to pass it shortly after.

�Congress absolutely should have the opportunity to review this deal,� the House speaker, John A. Boehner of Ohio, said Tuesday. �We shouldn�t just count on the administration, who appears to want a deal at any cost.�

White House officials blitzed Congress in the days after the framework of a nuclear deal was announced, making 130 phone calls to lawmakers, but quickly came to the conclusion that the legislation could not be blocked altogether.

Moreover, officials increasingly worried that an unresolved fight could torpedo the next phase of negotiations with Iran.

�Having this lingering uncertainty about whether we could deliver on our side of the deal was probably a deal killer,� said a senior administration official, who asked for anonymity to describe internal deliberations.

Under the compromise legislation, a 60-day review period of a final nuclear agreement in the original bill was in effect cut in half, to 30 days, starting with its submission to Congress. But tacked on to that review period potentially would be the maximum 12 days the president would have to decide whether to accept or veto a resolution of disapproval, should Congress take that vote.

The formal review period would also include a maximum of 10 days Congress would have to override the veto. For Republicans, that would mean the president could not lift sanctions for a maximum of 52 days after submitting a final accord to Congress, along with all classified material.

And if a final accord is not submitted to Congress by July 9, the review period will snap back to 60 days. That would prevent the administration from intentionally delaying the submission of the accord to the Capitol. Congress could not reopen the mechanics of a deal, and taking no action would be the equivalent of allowing it to move forward.

Mr. Corker also agreed to a significant change on the terrorism language.

Initially, the bill said the president had to certify every 90 days that Iran no longer was supporting terrorism against Americans. If he could not, economic sanctions would be reimposed.

Under the agreement, the president would still have to send periodic reports to Congress on Iran�s activities regarding ballistic missiles and terrorism, but those reports could not trigger another round of sanctions.

The measure still faces hurdles. Senator Marco Rubio of Florida, fresh off the opening of his campaign for the Republican presidential nomination, dropped plans to push for an amendment to make any Iran deal dependent on the Islamic Republic�s recognition of the State of Israel, a diplomatic nonstarter.

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But he hinted that he could try on the Senate floor.

�Not getting anything done plays right into the hands of the administration,� Mr. Rubio said.

Senator Ron Johnson, Republican of Wisconsin, abandoned an amendment to make any Iran accord into a formal international treaty needing two-thirds of the Senate for its ratification, but he, too, said it could be revived before the full Senate.

Mr. Earnest said the president also wanted no more changes. �We�re asking for a commitment that people will pursue the process that�s contemplated in this bill,� he said.

Democrats had implored Mr. Obama to embrace the legislation.

�If the administration can�t persuade 34 senators of whatever party that this agreement is worth proceeding with, then it�s really a bad agreement,� Senator Chris Coons of Delaware, a Democrat on the Foreign Relations Committee, said. �That�s the threshold.�

To temper opposition to the deal, Mr. Kerry, Treasury Secretary Jacob J. Lew and Energy Secretary Ernest J. Moniz gathered with senators Tuesday morning in a classified briefing, after a similar briefing on Monday for the House.

But the administration met firm opposition in both parties.

The agreement �puts Iran, the world�s worst state sponsor of terrorism, on the path to a nuclear weapon,� said Senator Tom Cotton, Republican of Arkansas, as he emerged from the briefing. �Whether that�s a matter of months or a matter of years, that�s a dangerous outcome not just to United States and allies like Israel but to the entire world.�

This article was written by Jonathan Weisman & Peter Baker for The New York Times on April 14, 2015.