Tehran announced the latest rollback of its commitments under the 2015 accord on Sunday following the US assassination of a top general.

Russia is one of the five remaining parties in the deal following the pullout by the US in 2018, with the other four being Britain, China, France and Germany.

"Keeping the broad agreements and ensuring their sustained implementation must remain a priority task for all partners," the Russian foreign ministry said in a statement.

It said the announcement by Tehran of a further rollback of its commitments, by foregoing the limit on the number of centrifuges, "does not carry any threat from the point of view of nuclear weapon proliferation".

Tehran has repeatedly said that the troubled deal can be rescued if parties can help it circumvent crippling US sanctions, and on Sunday it said it would return to its commitments if sanctions were lifted and Iran benefited.

Moscow pointed out "holes" in the approach to the deal by other parties. "We hope that the necessary outcomes will be achieved. A lot depends on our European colleagues," it said.

Russia "keeps full commitment" to the deal and is "ready to continue work" on it, the statement said, calling on "political will and a decisive collective response" from others.

"We are certain that when these challenges are overcome, the Iranian side will have no reason to deviate from the agreed-upon demands," it said.

Tensions between Tehran and Washington have spiked following the US drone strike in Iraq that killed Iranian general Qasem Soleimani.

Russia and Iran are allies in the conflict in Syria, having supported the Syrian government for years against the opposition, and Soleimani had been Iran's pointman in organising its forces and foreign proxies on the battlefield.

Russia's Defence Minister Sergei Shoigu on Monday spoke with the chief of Iranian General Staff Mohammad Bagheri on "avoiding escalation of the situation in Syria and the Middle East due to the murder" of Soleimani.