International Atomic Energy Agency (IAEA) chief Rafael Gross on Sunday held talks in Iran, where the two sides agreed that Tehran will continue to allow access to UN inspectors to its declared nuclear sites.

Russian foreign ministry spokeswoman Maria Zakharova said Moscow "welcomed" the development and hoped it "will help improve the overall political situation around Iran and its nuclear programme".

"The IAEA and Iran have made a tangible positive contribution to the formation of conditions for the start of a substantive conversation ... about Washington's return to the 'nuclear deal,'" Zakharova said.

"We call on all ... partners, as well as the United States, to act without delay," she added.

The deal, brokered in 2015 by then US President Barack Obama, saw Iran drastically scale back its nuclear programme in exchange for promises of economic relief.

But it has been on the brink of collapse since former US president Donald Trump withdrew from it nearly three years ago.

Tehran wants Washington to take the first step by scrapping sanctions Trump reimposed in 2018, while the United States insists Iran first return to all its nuclear commitments.

Moscow last week welcomed Washington's move to reverse two steps imposed by Trump, retracting calls for international sanctions on Tehran and removing curbs on Iranian diplomats in New York.