Parties to the Iran nuclear agreement on Saturday adjourned the third round of negotiations in Vienna aimed at bringing the United States back into the accord, with the Russian side expressing "cautious and growing optimism" and saying they hoped to achieve concrete results within three weeks.

The deal, which curbs Iran's nuclear programme in exchange for sanctions relief, has been on life support since then US president Donald Trump bolted in 2018.

The remaining partners to the 2015 accord have been engaged in negotiations since early April to try to revive it.

The third round of talks started on Tuesday and, after several days of technical discussions between expert groups, delegations met on Saturday.

Representatives of the parties still in the agreement (Iran, China, Russia, France, Germany, the United Kingdom) who met for just over an hour noted the "indisputable progress" achieved, Russian ambassador Mikhail Ulyanov said on Twitter adding that he was cautiously optimistic.

"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 three weeks. Is it realistic? We will see," he wrote.

The delegations would return to their respective capitals and resume talks from next Friday, Iran's foreign ministry said in a statement.

The Russian side expressed cautious optimism after the talks on Saturday and said they hoped for a result within three weeks
The Russian side expressed cautious optimism after the talks on Saturday and said they hoped for a result within three weeks EU DELEGATION IN VIENNA / Handout

"Considering the commission's previous decision regarding speeding up the talks process, this week's talks continued quickly in bilateral format and the sides tried to minimise disagreements regarding the texts.

"The sides agree that the work must continue with more speed and seriousness in the future round of talks."

A diplomatic source from the E3 powers of Britain, France and Germany said the talks had taken place in a "serious and focused atmosphere despite outside turbulences".

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

"As E3, we will redouble our efforts to make this deal possible."

Earlier, a European diplomat said that the American, European, Russian and Chinese delegations held a joint meeting on Saturday morning, but without Iranian representation as Tehran has refused to negotiate with the US directly.

As well as bolting from the accord, Trump's administration slapped sweeping sanctions on Iran, which in turn started ramping up its nuclear activities.

New US President Joe Biden supports the JCPOA -- the acronym for the agreement with which Iran was in compliance before Trump's sanctions -- but has called on Tehran to roll back its measures before Washington ends sanctions.