Russia and the United States have expressed hope that tense relationships could begin to improve.
With tensions running high over Iran, Syria, Ukraine and Venezuela, Russian President Vladimir Putin claimed he was informed of the investigation into Russia's involvement in the US presidential election in 2016 and said he thought it was time to move on.
Meanwhile, US Prime Minister Mike Pompeo transferred President Donald Trump's interest in restoring better ties.
At the highest level of face-to-face contact between the two countries, since Special Report Robert Mueller's report was released last month, Mr Putin told Mr Pompeo that he hoped that relations with the United States would now improve.
Nevertheless, his claim for justification covered only allegations that Russia and the Trump campaign collided to harm Hillary Clinton's candidacy. Sir. Putin did not accept Mr Mueller's conclusion that Russia was actively involved in the election.
"But the exotic Specialist's work was, I have to say, that he as a whole has had a very objective investigation, and he confirmed that there was no trace of the interaction between Russia and the established administration that we said was completely false," Putin when he opened the meeting with Mr Pompeo in the Black Sea resort of Sochi.
"As we said before, there was no co-operation from our officials, and it couldn't be there. Still, it was one of the reasons for that particular break in our intergovernmental ties," he said. "Today I hope the situation will change."
Sir. Pompeo did not specifically mention mediation in his brief answer to Putin, although he said the Trump administration would "protect our country's interest". Earlier, however, Mr Pompeo stated that any repetition of the 2016 interference would not be tolerated.
"Interference in US elections is unacceptable," Pompeo told reporters at a press conference with Russian Foreign Minister Sergey Lavrov.
"If Russia were to involve it in 2020, it would put our relationship in an even worse place than it is. We have urged them not. We would not tolerate it. Our choices are important and sacred and they must be free and fair . "
Having met with Mr Putin, Mr Pompeo told reporters: "So it's not about moving on. It's about trying to find solutions, compromises, places where there are overlapping interests you can make progress and unlock for some of the most difficult problems we face. "
Sir. Putin told Mr Pompeo that his recent telephone conversation with Mr Trump was hoping for an improvement in relations.
"As you know, not so long ago, I had the pleasure of talking to the US president by phone," he said.
"For me, it created the impression that the President intends to restore Russian-American relations and contacts to solve common problems that present common interests."
Sir. Pompeo talked about "truly overlapping interests", which the two countries "can build on, and most importantly, President Trump would like to do so".
He mentioned cooperation in Afghanistan and counter-terrorism more broadly, but also a common goal of getting North Korea to abandon nuclear weapons. But he also told Mr Putin that "like you will, we will protect our country's interest".