The United States on Sunday proposed extending an interim agreement with Iran in a recognition that talks to settle deep differences over Tehran’s nuclear program were unlikely to succeed before a deadline just one day away.

Secretary of State John F. Kerry formally raised the issue of an extension in an evening meeting with Iranian Foreign Minister Mohammad Javad Zarif, according to a senior State Department official. It was their second meeting on Sunday, a day in which Kerry shuttled between talks with European allies and the Iranian negotiating team.

An extension is one of several alternatives under discussion, the official said.

“This does not mean that we are not continuing to discuss the broad range of difficult issues and working to make progress on all the issues that need to be part of a comprehensive agreement,” the official said.

In addition to his meetings with his Iranian counterpart, Kerry held talks with the foreign ministers of Britain, France, Germany and Russia. China’s envoy was expected, as well, rounding out the group of nations negotiating with Iran to limit its nuclear capability in exchange for an easing of international sanctions on the country.

Nevertheless, there was growing acceptance that the remaining differences could not be bridged by midnight Monday. That is when an interim accord, already extended once, expires.

The hang-ups are few in number but wide in substance. One of the most important is how many uranium-enriching centrifuges and stockpiles Iran will be permitted to keep for what it insists are peaceful, civilian purposes. Divisions also remain over the pace at which sanctions would be eased if Iran makes concessions and over how many years the country’s nuclear program would be monitored.

On ABC’s Sunday talk show, “This Week,” President Obama said the interim agreement had successfully rolled back Iran’s nuclear capacity, but he expressed doubt about whether the “significant” gaps could be bridged to achieve a permanent accord.

“I think that our goal has consistently been to shut off a whole bunch of different avenues whereby Iran might get a nuclear weapon and at the same time make sure that the structure of sanctions are rolled back step for step as Iran is doing what it’s supposed to do,” he said. “I think Iran would love to see the sanctions end immediately and then to still have some avenues that might not be completely closed, and we can’t do that.”

A delay carries political complications for Washington and Tehran. It could hamper the Obama administration’s ability to get congressional approval for easing sanctions against Iran, with Republicans poised to gain control of Capitol Hill in January. It also could embolden Iranian hard-liners opposed to any agreement involving the United States.

The sanctions are hurting a broad spectrum of Iranian society, particularly as oil prices fall. But some Iranians remain reluctant to cede ground in the dispute, seeing nuclear reactors as crucial to their future.

A group of Iranian students protested Sunday at the site of a reactor in Tehran, demanding that Iran not cave in and reduce its nuclear capacity. According to the Fars News Agency, the students chanted, “Nuclear energy is our inalienable right.”

Recent analyses in the Iranian news media have portrayed Saudi Arabia, Iran’s regional rival, and Israel, often referred to as “the Zionist regime,” as the main roadblocks to a deal.

Kerry has kept both countries apprised of the talks. On Sunday, he went to the Vienna airport to update the Saudi foreign minister aboard his plane, which was sitting on the runway.

In Israel, where skepticism over a long-term deal with Iran is strong, Prime Minister Benjamin Netanyahu said at the weekly cabinet meeting Sunday that he was pressing a “vigorous” case that Iran not be allowed to become a “nuclear threshold state.”

“No agreement at all would be preferable to a bad agreement that would endanger Israel, the Middle East and all of humanity,” said Netanyahu, whom Kerry telephoned Saturday evening to give an update on the status of the talks.

William Booth in Jerusalem contributed to this report.