WASHINGTON — The United States and Iran have agreed for the first time to one-on-one negotiations over Iran’s nuclear program, according to Obama administration officials, setting the stage for what could be a last-ditch diplomatic effort to avert a military strike on Iran.

Iranian officials have insisted that the talks wait until after the presidential election, a senior administration official said, telling their US counterparts that they want to know which American president they would be negotiating with.

News of the agreement — a result of intense, secret exchanges between US and Iranian officials that date almost to the beginning of President Barack Obama’s term — comes at a critical moment in the presidential contest, just two weeks before Election Day and a day before the final debate, which is to focus on national security and foreign policy.

It has the potential to help Obama make a case that he is nearing a diplomatic breakthrough in the decade-long effort by the world’s major powers to curb Tehran’s nuclear ambitions, but it could also pose a risk if Iran is seen as using the prospect of the direct talks to buy more time.

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

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 Obama is re-elected. Iran has a long history of using the promise of diplomacy to ease international pressure on it. In this case, US officials said they were uncertain whether Iran’s opaque supreme leader, Ayatollah Ali Khamenei, had signed off. The US understandings have been reached with senior Iranian officials who report to him, an administration official said.

Even if the two sides sit down, US 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 US 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 Washington and Tehran since the American hostage crisis in 1979.

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

The question of how best to deal with Iran has political ramifications for Romney as well. While he has accused Obama of weakness, he has given few specifics about what he would do differently.

Moreover, the prospect of one-on-one negotiations could put Romney in an awkward spot, since he has opposed allowing Iran to enrich uranium to any level — a concession that experts say is likely to figure in any deal on the nuclear program.

Beyond that, how Romney responds could signal how he would act if he becomes commander in chief. The danger of opposing such a diplomatic initiative is that it could make him look as if he is willing to risk another US war in the Middle East without exhausting alternatives.

‘’It would be unconscionable to go to war if we haven’t had such discussions,’’ said R. Nicholas Burns, who led negotiations with Tehran as undersecretary of state in the George W. Bush administration.

Iran’s nuclear program ‘‘is the most difficult national security issue facing the United States,’’ he said, adding: ‘‘While we should preserve the use of force as a last resort, negotiating first with Iran makes sense. What are we going to do instead? Drive straight into a brick wall called war in 2013, and not try to talk to them?’’

The administration, officials said, has begun an internal review among officials at the State Department, the White House and the Pentagon to determine the US negotiating stance, and what the United States would put in any offer. One option under consideration is ‘‘more for more’’ — more restrictions on Iran’s enrichment activities in return for more easing of sanctions.