It is also far from clear that Mr. Obama’s opponent, Mitt Romney, would go through with the negotiation should he win election. Mr. Romney has repeatedly criticized the president as showing weakness on Iran and failing to stand firmly with Israel against the Iranian nuclear threat.

The White House denied that a final agreement had been reached. “It’s not true that the United States and Iran have agreed to one-on-one talks or any meeting after the American elections,” Tommy Vietor, a White House spokesman, said Saturday evening. He added, however, that the administration was open to such talks, and has “said from the outset that we would be prepared to meet bilaterally.”

Reports of the agreement have circulated among a small group of diplomats involved with Iran.

There is still a chance the initiative could fall through, even if Mr. Obama is re-elected. Iran has a history of using the promise of diplomacy to ease international pressure on it. In this case, American officials said they were uncertain whether Iran’s supreme leader, Ayatollah Ali Khamenei, had signed off on the effort. The American understandings have been reached with senior Iranian officials who report to him, an administration official said.

Even if the two sides sit down, American officials worry that Iran could prolong the negotiations to try to forestall military action and enable it to complete critical elements of its nuclear program, particularly at underground sites. Some American officials would like to limit the talks to Iran’s nuclear program, one official said, while Iran has indicated that it wants to broaden the agenda to include Syria, Bahrain and other issues that have bedeviled relations between Iran and the United States since the American hostage crisis in 1979.

“We’ve always seen the nuclear issue as independent,” the administration official said, speaking on the condition of anonymity because of the delicacy of the matter. “We’re not going to allow them to draw a linkage.”