The Senate gave overwhelming approval Thursday to legislation that would establish a congressional review for a proposed nuclear deal with Iran, as Republican leaders set aside efforts from their own rank and file to amend the carefully crafted bipartisan compromise.

On a 98-to-1 vote, the Senate lent a bipartisan boost to the measure — which the House is likely to approve next week — that would allow for a 30-day review of any final deal with Iran, giving what supporters said is a congressional voice to the process as President Obama finishes negotiations with the Islamic republic.

“Without this bill, there is no review,” Sen. Bob Corker (R-Tenn.), chairman of the Senate Foreign Relations Committee, said during the closing debate, which shut off a bid from younger conservatives to toughen the language even if meant a collapse of support for the oversight. “No bill, no review.”

The victory presented Senate Majority Leader Mitch McConnell (R-Ky.) with a decision of whether to scuttle the efforts of his party’s young conservative stars — particularly Sens. Tom Cotton (Ark.) and Marco Rubio (Fla.), a presidential candidate — to keep Democrats and Obama supportive of the proposal.

“Many wish the bill was stronger. I don’t disagree with them, but this is a piece of legislation worthy of our support,” McConnell said Wednesday during a floor speech. “It offers the best chance we have to provide the American people and the Congress they elect with power to weigh in on a vital issue.”

McConnell has been leader for barely four months, and maneuvering this week has been his most serious challenge in dealing with the staunch conservative wing of his caucus — the sort of entanglements that have repeatedly bedeviled his House counterpart, Speaker John A. Boehner (R-Ohio), for the past four years.

But much of the negotiating fell to Corker. He had spent Tuesday night on the phone with Cotton, who in his four months in the Senate has emerged as a conservative favorite for his anti-Obama posture on foreign policy.

“He agreed to stand down,” Corker told reporters Wednesday, praising the Bronze Star recipient’s willingness not to use every procedural delaying tactic at his disposal.

The final votes came together quickly Thursday after 24 hours of jousting over continued efforts by conservatives to push their amendments. Once McConnell and Senate Minority Leader Harry M. Reid (D-Nev.) agreed to move ahead Thursday, almost all opposition disappeared.

Just six Republicans, including Cotton and Sen. Ted Cruz (Tex.), opposed the procedural vote to move to final passage of the bill.

The consensus legislation — which Corker brokered in almost three months of negotiating with Democrats — would give Congress 30 days to review a nuclear pact with Iran. During that time, Obama would be able to waive sanctions against Tehran that were imposed by the executive branch but would have to leave in place sanctions that Congress previously drafted.

If the House and the Senate passed resolutions disapproving of the Iran deal, including overcoming a possible presidential veto, then Obama would be forced to leave in place those congressionally mandated sanctions. Any other outcome, including a deadlock in which the legislation just stalls with no clear outcome, would allow Obama to go ahead with implementing all aspects of any nuclear deal.

Corker won over enough Democrats with slight modifications to the bill that Obama dropped his veto threat and his committee approved it unanimously.

However, once the bill landed on the full Senate floor last week, the younger crop of GOP conservatives sought to toughen up the measure regardless of whether Democrats would abandon it. Some Republicans, including Rubio and Cruz, are running for their party’s presidential nomination in 2016, and Reid skewered their actions over the past week as attempts to court conservative primary voters rather than passing the legislation.

But the driving force of late has been Cotton, who earlier this year irked Corker and his Democratic colleagues when he wrote a letter to Iranian leaders warning them not to finalize a nuclear deal with the Obama administration because a future Republican president would invalidate it. He got 46 other Republicans to sign it.

Cotton has proposed inserting language that would make any deal contingent on a certification that Iran is not engaging in terrorist activities against Americans, while Rubio is seeking to condition the deal on Iran recognizing Israel as a state for the first time. The Obama administration has opposed both provisions, saying they could derail efforts to contain Iran’s nuclear weapons ambitions, setting up a likely veto.

Cotton used a rare procedural move against his own leadership team that left McConnell with two options: allow Cotton’s Israel amendment to come up and probably see the entire underlying bill fall apart, or use his privileges to shut down the amendment process and just advance the Corker measure toward a final vote.

McConnell took that unusual step of shutting down the amendment process to protect Democrats from having to vote on Republican ideas.

In a statement, Cotton blamed Democrats — not McConnell — for sinking his amendment, saying, “Congress must stand up and protect America from a nuclear Iran, and it’s regrettable that Democratic intransigence blocked our efforts to strengthen this bill.”

During votes Tuesday evening, Corker huddled with Cotton and Rubio for several minutes on the Senate floor and then spoke by phone later.

“It’s time to move on,” Corker told reporters Tuesday. “If we’re going to pass the bill, we need to get on with it, and we’ve got other business we want to move to.”

McConnell has announced his intention to take up trade legislation immediately after the Iran bill. Obama is seeking a renewal of “trade promotion authority” giving him a freer hand to negotiate international agreements — powers that, in a twist, most Republican lawmakers support and most Democrats oppose.

Although some conservatives are still fighting to amend the Iran bill, some Democrats have considered forcing McConnell to burn up the clock on every procedural motion to prevent a vote on the Corker bill until late next week — only so that they can delay consideration of the trade bill.