"It's evident that these negotiations are really not P5+1 negotiations any more," Senate Foreign Relations Committee Chairman Bob Corker said as he emerged from a closed-door briefing by Obama administration officials on the status of nuclear talks with Iran.
"It's really more of a bilateral negotiation between the United States and Iran."
The five permanent UN Security Council members -- Britain, China, France, Russia and the United States -- plus Germany have undertaken years-long talks with Iran in a bid to halt the Islamic republic's nuclear drive.
Several rounds of sanctions have been imposed on Iran, cutting deeply into the country's economy.
Under an interim agreement reached in November 2013, Iran has diluted its stock of fissile materials from 20 percent enriched uranium to five percent in exchange for limited sanctions relief.
But two deadlines for a permanent agreement have already been missed, requiring the talks to be extended.
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President Barack Obama met with German Chancellor Angela Merkel at the White House on Monday, and Obama said he saw no reason to further extend the current deadlines.
The present issue, Obama said, was "does Iran have the political will and the desire to get a deal done?"
With an end-March deadline for a political agreement approaching, and a final deal confirming technical details required by June 30, Corker said the key players are now essentially Washington and Tehran.
"I was in Munich this weekend (for an international security conference) and was very aware that this was becoming more of a one-on-one negotiation," the Senate Republican told reporters.
Corker and the Democrat he replaced as committee chairman, Senator Robert Menendez, left the latest briefing expressing concern about the administration basing negotiations on the need to maintain Iran's potential nuclear weapons "breakout" time to at least one year.
"One of my major concerns all along that is becoming more crystal clear to me, is that we are, instead of preventing proliferation, we are managing proliferation," Menendez said.
Having Iran just one year away from building a bomb would be "a different world and a far more challenging world," he added.