The Vienna talks, which involve Iran as well as Britain, China, France, Germany and Russia directly, and the United States indirectly, resumed in late November with the aim of restoring the 2015 deal.

That accord had offered Tehran sanctions relief in exchange for curbs on its nuclear program, but the United States unilaterally withdrew in 2018 under former president Donald Trump and reimposed heavy economic sanctions, prompting Iran to begin rolling back on its commitments.

Stating that "substantial progress has been made in the last week," a State Department spokesperson told AFP that "if Iran shows seriousness, we can and should reach an understanding on mutual return to full implementation of the JCPOA within days," using an acronym for the 2015 deal.

But "anything much beyond that would put the possibility of return to the deal at grave risk," the spokesperson added.

Experts believe Iran is only a few weeks away from having enough fissile material to build a nuclear weapon -- even if it would take several more complicated steps to create an actual bomb.

President Joe Biden said he is willing to return to the deal and ease some of the US sanctions, provided Tehran resumes its commitments under the agreement.

France had warned Iran Wednesday that time was running out to accept a new deal. Foreign Minister Jean-Yves Le Drian said it was "a question of days," adding that a major crisis would be unleashed if there is no agreement.

But earlier in the day, Iran's top negotiator Ali Bagheri said they "are closer than ever to an agreement."

He called on the other parties to be "realistic" and make "serious decisions."

Tehran also called on the US Congress to say Washington would commit if an agreement is reached in Vienna.

Iranian authorities had said in 2018 they wanted a "guarantee" that an agreement would be implemented, as the potential of US political turnover had once more brought that into question.