By Steve Holland and Vladimir Soldatkin

WASHINGTON/MOSCOW (Reuters) - Russia has offered to mediate between the United States and Iran, a source briefed on discussions told Reuters on Tuesday, as the Kremlin vowed to do everything possible to facilitate a peaceful solution to tensions over Tehran's nuclear program.

Russia's state-run Zvezda media outlet reported earlier on Tuesday, citing Kremlin spokesman Dmitry Peskov, that President Vladimir Putin had agreed to mediate between Tehran and Washington in talks over nuclear weapons.

A source briefed on the discussions, speaking on condition of anonymity, told Reuters that Russia had offered to act as an intermediary, but Moscow was not asked to serve in such a role.

Iran's mission to the United Nations in New York declined to comment.

The development comes after U.S. President Donald Trump upended U.S. policy after taking office in January, taking a more conciliatory stance towards Russia that has left Western allies wary as he tries to broker an end to Moscow's three-year war in Ukraine.

Peskov told reporters on Tuesday that Iran was Russia's partner and ally and Moscow would continue to develop relations.

"President Putin believes and is convinced that the problem of Iran's nuclear dossier should be solved solely by peaceful means," he said. "Of course, Russia, being an Iranian ally, will be doing all what is possible to facilitate the peaceful solution to the problem."

Trump last month restored his "maximum pressure" campaign on Iran in a bid to stop Tehran from building a nuclear weapon. But he also said he was open to a deal and was willing to talk to Iran's President Masoud Pezeshkian.

"The Trump administration will talk to our adversaries and allies alike, but ... from a position of strength to defend our national security," Brian Hughes, spokesperson for the White House National Security Council, said on Tuesday.

SANCTIONS 'SNAPBACK'

Iran has denied wanting to develop a nuclear weapon. However, it is "dramatically" accelerating enrichment of uranium to up to 60% purity, close to the roughly 90% weapons-grade level, the U.N. nuclear watchdog has warned.

Western states say there is no need to enrich uranium to such a high level under any civilian program and that no other country has done so without producing nuclear bombs. Iran says its nuclear program is peaceful.

"The United States will not tolerate Iran obtaining a nuclear weapon or their support of terror in the Middle East and around the world," Hughes said.

U.S. Secretary of State Marco Rubio spoke with Israeli Prime Minister Benjamin Netanyahu on Tuesday, conveying "that he anticipates close coordination in addressing the threats posed by Iran and pursuing opportunities for a stable region," State Department spokesperson Tammy Bruce said.

Iran agreed a deal in 2015 with Britain, Germany, France, the U.S., Russia and China - known as the Joint Comprehensive Plan of Action (JCPOA) - that lifted sanctions on Tehran in return for restrictions on its nuclear program.

Washington quit the agreement in 2018 during Trump's first term as president, and Iran began moving away from its nuclear-related commitments.

Britain, France and Germany have told the U.N. Security Council that they are ready - if needed - to trigger a so-called "snap back" of all international sanctions on Iran to prevent the country from acquiring a nuclear weapon.

They will lose the ability to take such action on October 18 next year when the 2015 U.N. resolution on the deal expires. Trump has directed his U.N. envoy to work with allies to snapback international sanctions and restrictions on Iran.

(Reporting by Steve Holland and Vladimir Soldatkin; Writing by Michelle Nichols; Editing by Katharine Jackson and Daniel Wallis)