WASHINGTON — The fractious debate over a possible nuclear deal with Iran escalated on Monday as 47 Republican senators warned Iran about making an agreement with President Obama, and the White House accused them of undercutting foreign policy.

In a rare direct congressional intervention into diplomatic negotiations, the Republicans signed an open letter addressed to “leaders of the Islamic Republic of Iran” declaring that any agreement without legislative approval could be reversed by the next president “with the stroke of a pen.”

The letter appeared aimed at unraveling a framework agreement even as negotiators grew close to reaching it. Mr. Obama, working with leaders of five other world powers, argues that the pact would be the best way to keep Iran from obtaining a nuclear bomb. But critics from both parties say that such a deal would be a dangerous charade that would leave Iran with the opportunity to eventually build weapons that could be used against Israel or other foes.

While the possible agreement has drawn bipartisan criticism, the letter, signed only by Republicans, underscored the increasingly party-line flavor of the clash. Just last week, the Republican House speaker, John A. Boehner, gave Prime Minister Benjamin Netanyahu of Israel the platform of a joint meeting of Congress to denounce the developing deal, and Senate Republicans briefly tried to advance legislation aimed at forcing Mr. Obama to submit it to Congress, alienating Democratic allies.