US Secretary of State Mike Pompeo has told Russia that Washington would brook no interference in the 2020 US presidential election.
He also said he wanted Moscow to take action to show there would be no repeat of its suspected 2016 meddling.
President Vladimir Putin, who met Pompeo in the Russian Black Sea resort of Sochi, pushed back, telling him that Russia never interfered in US elections and that a report by US Special Counsel Robert Mueller, which he praised as being "objective overall", did not establish there was collusion with President Donald Trump's 2016 campaign.
Now that the Mueller report was out of the way, something which had long cast a pall over US-Russia relations, Putin said he hoped ties would start improving.
"I've formed the impression that your president wants to repair Russia-US ties and contacts and wants to solve issues which are of common interest for us," Putin told Pompeo.
"We've said many times that we also want to fully restore our relations. I hope that the necessary conditions for that to happen will now be created."
Visiting Russia for the first time as secretary of state, Pompeo had earlier clashed with Russian Foreign Minister Sergei Lavrov on issues from Ukraine to Venezuela. After their meeting, both men said they had been far apart on many issues.
"I made clear to Foreign Minister Lavrov ... that interference in American elections is unacceptable. If the Russians were engaged in that in 2020, it would put our relationship in an even worse place than it has been," said Pompeo.
"I'd encourage them not to do that. We would not tolerate that."
Both Lavrov and Pompeo said they shared a desire to improve battered ties despite not being able to confirm a suggestion by Trump that he would meet Putin on the sidelines of a meeting of the G20 in Japan next month.
Putin would agree to such a meeting if formally asked, a Kremlin aide told reporters.
"The United States stands ready to find common ground with Russia as long as the two of us can engage seriously," Pompeo said.
"President Trump has made clear that his expectation is that we will have an improved relationship. This will benefit each of our peoples. And I think that our talks here today were a good step in that direction."
A Kremlin aide said the talks had not yielded any breakthrough but had been held in a business-like atmosphere.
Relations have long been strained by US intelligence and law enforcement findings - denied by Moscow - that Russia tried to influence the results of the 2016 US presidential election to boost Trump's chances of winning the White House.