Photo taken on March 29, 2015 shows the general view of the plenary session on Iran's potential nuclear framework deal in Lausanne, Switzerland. Foreign ministers from major world powers on Sunday night kicked off a plenary session to further bridge gaps on Iran's potential nuclear framework deal. [Photo/Xinhua]

Officials had hoped to wrap up the current talks by Tuesday night with that joint general statement agreeing to start a new phase of negotiations to curb Iran's nuclear program. That statement would be accompanied by more detailed documents that would include technical information on understandings of steps required on all sides to resolve outstanding concerns.

Those documents would allow the sides to claim that the new phase of talks would not simply be a continuation of negotiations that have already been twice extended since an interim agreement between Iran and the so-called P5+1 nations was concluded in November 2013.

President Barack Obama and other leaders have said they are not interested in simply a third extension.

The softening of the language from a framework "agreement" to a framework "understanding" appeared due in part to opposition to a two-stage agreement from Iran's supreme leader, Ayatollah Ali Khamenei. Earlier this year, he demanded only one deal that would nail down specifics and not permit the other side to "make things difficult" by giving it wiggle room on interpretations.

But if the parties agree only to a broad framework that leaves key details unresolved, Obama can expect stiff opposition at home from members of Congress who want to move forward with new, stiffer Iran sanctions. Lawmakers had agreed to hold off on such a measure through March while the parties negotiated.

The White House says new sanctions would scuttle further diplomatic efforts to contain Iran's nuclear work and possibly lead Israel to act on threats to use military force to accomplish that goal.

Critics will likely accuse the Obama administration of backing away from promises of a tougher March agreement.

Sen. Tom Cotton, R-Ark., said Tuesday that extending the talks "proves once again that Iran is calling the shots." He said the Obama administration has made "dangerous concessions" to the Iranians over the past week, though he did not specify them.

"The best solution is walk away from the nuclear negotiations now and return to a position of strength," Cotton said in a written statement. He said the US should reinstate existing sanctions that have been suspended, and Congress "should act immediately to impose new sanctions."

In a letter signed by Cotton and 46 other Republican senators in early March, the lawmakers warned Tehran that any nuclear agreement with the Obama administration that lacks congressional approval could be unraveled by future presidents.