WASHINGTON — In a reprieve for President Obama, Democrats in Congress who support legislation that gives Congress the authority to review his emerging nuclear deal with Iran pledged Wednesday to wait to press their case until after a March 24 negotiating deadline between the two nations.

Angered by Republican efforts to speed action on bipartisan legislation that could tie Mr. Obama’s hands in the nuclear talks, the Democrats said they would withhold their votes on the bill until after the date set for reaching a political framework for a negotiated agreement with Iran.

The move by Senator Robert Menendez of New Jersey and eight other Democrats, as well as Senator Angus King, an independent of Maine, effectively freezes in place efforts to build a bipartisan coalition that would force a congressional review of any Iran deal.

For the president, the action merely postpones what is emerging as a steep challenge to one of his most important foreign policy priorities. There is a growing bipartisan coalition of lawmakers in Congress who believe they must have a say over any final agreement — if one is reached — to prevent Iran from acquiring nuclear weapons, and they are moving aggressively to lay out tough requirements for Mr. Obama that could shape any deal.