Presidents Donald Trump and Vladimir Putin have met face to face for the first time at the G20 summit in Hamburg, Germany.
They have discussed the alleged Russian hacking of last year’s US presidential election.
Secretary of State Rex Tillerson described the exchanges as “robust”.
And Russian Foreign Minister Sergei Lavrov said President Trump had accepted President Putin’s assertions that Russia was not responsible.
However, Rex Tillerson said it was not clear whether the US and Russia would ever come to an agreement on what happened.
“I think the president is rightly focused on how do we move forward from something that may be an intractable disagreement at this point,” the secretary of state added.
Donald Trump and Vladimir Putin held their first face-to-face talks on the sidelines of the G20 summit, which is being held amid sometimes violent protests.
Other topics discussed during their meeting – which lasted nearly two-and-a-quarter hours, longer than originally planned – included the war in Syria, terrorism and cybersecurity.
Rex Tillerson, part of the US delegation, told reporters afterwards: “The president opened the meeting with President Putin by raising the concerns of the American people regarding Russian interference in the 2016 election.”
“They had a very robust and lengthy exchange on the subject. The president pressed President Putin on more than one occasion regarding Russian involvement.
“President Putin denied such involvement, as I think he has done in the past.”
Rex Tillerson said the two leaders had “connected very quickly”, adding: “There was a very clear positive chemistry between the two. There are so many issues on the table… Just about everything got touched upon… Neither one of them wanted to stop.
“I believe they even sent in the First Lady [Melania Trump] at one point to see if she could get us out of there, but that didn’t work either… We did another hour. Clearly she failed!”
Sergei Lavrov told reporters: “President Trump said he heard clear statements… that Russian authorities did not intervene [in the US election], and he accepted these declarations.”
Rex Tillerson was asked as he was leaving the news conference if this was accurate, but declined to answer.
Earlier, as the talks began in front of the media before going into private session, President Trump told President Putin: “It’s an honor to be with you.”
President Putin replied: “I’m delighted to meet you personally.”
Donald Trump added: “Putin and I have been discussing various things, and I think it’s going very well.
“We’ve had some very, very good talks. We’re going to have a talk now and obviously that will continue. We look forward to a lot of very positive things happening for Russia, for the United States and for everybody concerned.”
Vladimir Putin, via a translator, said that while they had previously spoken by phone, that would never be as good as meeting face to face.
The G20 (Group of Twenty) is a summit for 19 countries, both developed and developing, plus the EU.