Ties between Moscow and Washington sank to a post-Cold War low following Russia's annexation of Crimea in 2014 and the allegations of its meddling in the US presidential election last year.
The Kremlin's hopes for warmer dealings under President Donald Trump have withered amid the Congressional and FBI investigations into alleged links between Trump's campaign and Russia.
The two countries introduced tit-for-tat measures to rebuke each other all year, ranging from restrictions on embassy staff to legislation targeting state-owned media.
Russia has denied any interference in the US election, and Peskov noted that the Kremlin is watching the ongoing US investigations with "bewilderment."
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"It's the US internal business, but it certainly hurts bilateral relations and we regret that," he said.
Peskov reiterated the Kremlin's position that Russia seeks good relations with the US based on "mutual trust and mutual respect," but added that "it takes two to tango."
Russian officials and lawmakers last week expressed dismay with the US decision to provide Ukraine with lethal weapons, including anti-tank missiles, warning the move would only fuel hostilities in eastern Ukraine.
"I don't see an evolving US military role in Ukraine," Mattis said. "Right now, we have some trainers there helping to train their army to NATO standards, and that has a lot to do with making certain it serves the needs of the Ukrainian people, in the way democracies' armies do, so the U.S. military role remains the same.