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Senator Mitch McConnell, the Republican majority leader, changed course Thursday in the face of opposition from Democrats and opted against pushing ahead with a bipartisan bill that would give Congress the authority to review any nuclear deal with Iran.

The legislation was drafted by Senator Robert Menendez, Democrat of New Jersey, and Senator Bob Corker, Republican of Tennessee. While the legislation has support from members of both parties, Democrats were angered by Mr. McConnell’s decision to hold a procedural vote on the bill as early as next Tuesday and threatened to delay it with a filibuster.

“While the original schedule would have allowed for a committee markup and vote on the Iran Nuclear Agreement Review Act of 2015 before final floor consideration, it is clear that Senate Democrats will filibuster their own bill — a bill they rushed to introduce before the White House cut a deal with Iran,” said Don Stewart, a spokesman for Mr. McConnell.

As The Times reported, Democrats announced Wednesday that they would wait to press their case on the bill until after the March 24 negotiating deadline between the United States and Iran.

The White House has said that President Obama would veto the legislation, which would require the president to submit any agreement to Congress and restrict his authority to waive sanctions for 60 days to give lawmakers time to weigh in.

Senator Harry Reid of Nevada, the minority leader, praised Mr. McConnell’s move in delaying a vote.

“Senator McConnell made the right decision by heeding calls from Democrats and Republicans to back off his transparently political move,” Mr. Reid said. “Protecting Israel and the world from a nuclear-armed Iran is too important of an issue to use in partisan political games.”

A new date for the vote has not been set.