Moscow
The Kremlin was responding to comments Trump made to Fox News in an interview aired at the weekend in which he complained that Iran had "total disregard" for the United States.
Kremlin spokesman Dmitry Peskov said in a conference call with reporters that Moscow saw things differently.
"Russia has friendly partner-like relations with Iran, we cooperate on a wide range of issues, value our trade ties, and hope to develop them further," said Peskov.
Trump and Putin say they want to try to rebuild U.S.-Russia ties, that were badly damaged by Moscow's 2014 annexation of Crimea and by Western sanctions imposed on Russia in response.
Peskov said there was no reason for policy differences over Iran to hinder such a rapprochement.
"It's no secret for anyone that Moscow and Washington hold diametrically opposed views on many international issues," said Peskov. "That should not be an obstacle when it comes to forging normal communication and pragmatic mutually-beneficial relations between Russia and the United States."
Separately, Russia criticized the Trump administration's move on Friday to impose sanctions on Iran after a recent ballistic missile test, saying the test did not violate existing agreements.
"We are sorry that things are working out in this way," Sergei Ryabkov, Russia's deputy foreign minister, was quoted as saying of the new sanctions by the RIA news agency on Monday.
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