Trump said Monday the two sides had, over the last two days, held "very good and productive conversations regarding a complete and total resolution of our hostilities."

Trump also said he had ordered a halt to threatened strikes on Iranian energy infrastructure, after earlier issuing an ultimatum for Iran to reopen the Strait of Hormuz.

The waterway has remained effectively closed since the start of the war sparked on February 28 by US-Israeli bombardment of Iran.

In a call with Iranian Foreign Minister Abbas Araghchi, Russia's top diplomat Sergei Lavrov urged an "immediate cessation of hostilities and a political settlement that takes into account the legitimate interests of all parties involved, above all Iran," the Russian foreign ministry said in a readout of the call.

There was no mention of US-Iran talks -- which have not been confirmed by Tehran -- in the Russian statement.

Moscow said the call was initiated by Iran.

Russia is one of the Islamic Republic's closest allies and has slammed the US-Israeli strikes on the country, but has not publicly offered military support.

Kremlin spokesman Dmitry Peskov had earlier said the "situation should have transitioned to a political and diplomatic settlement."

"This is the only thing that can effectively contribute to defusing the catastrophically tense situation that has now developed in the region," Peskov told reporters at a briefing.

He was speaking before Trump's statement that talks had taken place.

Russia -- which helped build Iran's only operational nuclear power plant at Bushehr -- has warned against strikes that could endanger the site that the UN's nuclear watchdog announced last week was hit by a projectile.

"Of course, this poses a very serious security threat if this trend continues," Peskov said Monday.

"We consider strikes on nuclear facilities to be potentially extremely dangerous and fraught with, perhaps even irreversible, consequences," he added.