In an open letter to Iranian leaders, Sen. Tom Cotton and 46 other Republicans said that without congressional approval, any deal between Iran and the US would be merely an agreement between President Barack Obama and Iran's supreme leader, Ayatollah Ali Khamenei.
"The next president could revoke such an executive agreement with the stroke of a pen," they wrote, "and future Congresses could modify the terms of the agreement at any time."
The White House called the a "continuation of a partisan strategy" to undermine Obama's foreign policy strategy.
Republican senators warned Iran that any nuclear deal made with Obama could last only as long as he remains in office, a warning that "certainly interferes in that effort" of the United States and its international partners to negotiate a nuclear deal with Iran, White House spokesman Josh Earnest told reporters in a briefing.
The US and other nations are seeking a pact that would let Western powers verify that Iran will not obtain a nuclear weapon.
Though the five-paragraph letter is addressed to leaders in Tehran, it seems as much aimed at delivering a message to Obama.
Republicans and some Democrats want Congress to vote on any agreement. The pact the bargainers are working on does not require congressional approval because it is not a treaty, which would require a two-thirds majority Senate vote to be ratified.
Last week, Senate Majority Leader Mitch McConnell postponed action on legislation that would give Congress a vote on any deal that emerges. He delayed the measure in the face of solid Democratic opposition to moving ahead on the bill now, just weeks before an end-of-March deadline for negotiators to produce an outline of an agreement.
On CBS' "Face the Nation" Sunday, McConnell said the president would need congressional approval to lift sanctions already imposed on Tehran because of its nuclear program.
"I think he cannot work around Congress forever," McConnell said.
Obama said in a separate CBS interview that the US would "walk away" from the talks unless they produce a procedure for verifying that restrictions on Iran's nuclear effort are working.
The letter released Monday was signed by 47 of the Senate's 54 Republicans.
The next negotiations are scheduled for March 15, and wide gaps remain between the two sides. Iran has said its nuclear program is peaceful and is aimed at producing energy. There was no immediate Iranian government reaction to the letter or any discussion of it in Iranian media.
Cotton is a freshman senator who serves on the Senate's Armed Service and Intelligence committees.