"The president opened the meeting with President Putin by raising the concerns of the American people regarding Russian interference in the 2016 election," Tillerson told reporters after the meeting on the sidelines of the G20 in Germany.
"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," Tillerson told reporters.
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Tillerson, who was present at the marathon two-and-a-quarter-hour meeting in Hamburg, said also that the two leaders "connected very quickly" at their talks on the sidelines of the G20 summit.
"There was a very clear positive chemistry between the two," Tillerson told reporters.
"There are so many issues on the table... Just about everything got touched upon... Neither one of them wanted to stop," he said.
"I believe they even sent in the [US] First Lady 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!"
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Tillerson's counterpart, Russian Foreign Minister Sergei Lavrov, said separately that Trump "accepted" Putin's denials of any involvement in the US election.
"President Trump said he heard clear statements from Putin that [the allegations of meddling] are not true, and that Russian authorities did not intervene, and he accepted these declarations," Lavrov said.
Asked as he was leaving the news conference if this was accurate, Tillerson refused to answer.
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