Diplomats from Britain, China, Germany, France and Russia have made progress at talks aimed at bringing the US back into their nuclear deal with Iran but say more work is needed to secure a future agreement.

After the meeting on Saturday, Russia’s top representative Mikhail Ulyanov tweeted that members of the Joint Comprehensive Plan of Action (JCPOA) “noted today the indisputable progress made at the Vienna talks on restoration of the nuclear deal”.

“The Joint Commission will reconvene at the end of the next week,” Mr Ulyanov wrote. “In the meantime, experts will continue to draft elements of future agreement.”

“It’s too early to be excited, but we have reasons for cautious and growing optimism. There is no deadline, but participants aim at successful completion of the talks in approximately 3 weeks.”

The three Western European countries involved in the talks struck a more restrained note.

“We have much work and little time left. Against that background, we would have hoped for more progress this week,” the senior diplomats said, speaking on condition of anonymity.

“We have yet to come to an understanding on the most critical points. Success is by no means guaranteed, but not impossible.”

In Washington, the US State Department had no immediate comment on reports of progress. It said the US assessment of the talks had not changed since Thursday, when State Department spokesman Ned Price said there had been some movement but that an agreement was far from done or even guaranteed.

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Russia’s Governor to the International Atomic Energy Agency Mikhail Ulyanov, addresses the media as he leaves the talks (Lisa Leutner/AP)

Abbas Araghchi, Iran’s deputy foreign minister, participated in the Vienna talks.

“I can say that now our discussions have reached a maturity, both in the disputed topics and in the sections that we are agreed on,” he told Iranian state TV. “Although we cannot yet fully predict when and how we will be able to reach an agreement, it is moving forward, although slowly.”

The US did not have a representative at the main table in Vienna because former President Donald Trump unilaterally pulled the country out of the deal in 2018. Mr Trump also restored and augmented sanctions to try to force Iran into renegotiating the pact with more concessions.

President Joe Biden wants to rejoin the deal, however, and a US delegation in Vienna was taking part in indirect talks with Iran, with diplomats from the other world powers acting as go-betweens.

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The ambassador of the Permanent Mission of China to the UN, Wang Qun, leaving the talks (Lisa Leutner/AP)

The Biden administration is considering a rollback of some of the most stringent Trump-era sanctions in a bid to convince Iran to come back into compliance with the nuclear agreement, according current and former US officials and others familiar with the matter.

Mr Ulyanov said JCPOA members met on the sidelines with officials from the US delegation but the Iranian delegation was not ready to meet with US diplomats.

The nuclear deal promised Iran economic incentives in exchange for curbs on its nuclear programme.

The re-imposition of US sanctions has left the Islamic Republic’s economy reeling. Tehran has responded by steadily increasing its violations of the deal, such as increasing the purity of uranium it enriches and its stockpiles, in a thus-far unsuccessful effort to pressure the other countries to provide relief from the sanctions.

The ultimate goal of the deal is to prevent Iran from developing a nuclear bomb, something it insists it does not want to do. Iran now has enough enriched uranium to make a bomb, but nowhere near the amount it had before the nuclear deal was signed.