The decision could halt the march of legislation that would levy more sanctions on Iran if no diplomatic agreement can be reached to prevent Tehran from being able to develop a nuclear weapon. Republicans could still push sanctions legislation – but without Democratic support, Congress would not likely have the votes needed to override a veto threatened by President Barack Obama.
Last week, House of Representatives Speaker John Boehner invited Prime Minister Benjamin Netanyahu to address a joint session of Congress in March and discuss the threats from Iran and radical Islam.
The Israeli prime minister's visit to Washington has opened up a political rift in the United States and has drawn accusations in Israel that Netanyahu is undermining a strategic alliance to win an election due to take place shortly after the planned speech.
The latest Democratic declaration on the sanctions appears intended to show that congressional Democrats are supporting the policy of their president.
Obama said if there is new sanctions legislation, Iran could walk away from the negotiating table, saying the "United States was operating in bad faith and blew up the deal." And he said the willingness of America's international partners to enforce existing sanctions against Iran would wane.
Diplomatic talks have been extended until July, with the goal of reaching a framework for a deal by the end of March.
Sen. Bob Menendez, a Democrat who drafted the legislation with Sen. Mark Kirk, a Republican, said at a Senate banking committee hearing that he and many of his Democratic colleagues had sent a letter to President Barack Obama saying they won't support passage of the bill until after March 24.
"The legislation that Sen. Kirk and I have drafted would signal to the Iranian regime that there will be more consequences if they choose not to reach a final deal," Menendez said.
"This morning, however, many of my Democratic colleagues and I sent a letter to the president, telling him that we will not support passage of the Kirk-Menendez bill on the Senate floor until after March 24 and only if there is no political framework agreement because, as the letter states, we remain hopeful that diplomacy will succeed in reversing Iran's ability to develop a nuclear weapon capability."
Menendez said the letter also states, however, that they remain very skeptical that Iran is committed to making the concessions necessary to demonstrate to the world that its nuclear program is exclusively peaceful by March 24.
Yitzhak Benhorin, Reuters, and the Associated Press contributed to this report.