U.S. President Donald Trump said Wednesday that Iran had agreed not to possess nuclear weapons, signaling potential progress in talks, as Tehran confirmed it is reviewing a U.S. proposal to end the war despite unresolved key demands.

"Look and this is very simple. Iran cannot have a nuclear weapon because as tough as they are, we want to keep them alive. We want to keep all of you alive," he told reporters at the White House.

"Iran cannot have a nuclear weapon, and they won't, and they've agreed to that, among other things. We've had very good talks over the last 24 hours, and it's very possible that we'll make a deal."

He added that Tehran had also agreed on other points, but did not provide further details.

Earlier, Iranian Foreign Ministry spokesman Esmail Baghai played down reports suggesting an agreement was close, calling them exaggerated.