Vladimir Putin and Donald Trump. Carlos Barria/Reuters US Secretary of State Rex Tillerson said Friday that President Donald Trump "pressed" Russian President Vladimir Putin on findings that Russia interfered in the 2016 presidential election, during what Tillerson described as a "very robust and lengthy exchange on the subject."

Tillerson said Russian meddling was discussed right at the onset of the pair's first bilateral meeting, at the G-20 summit in Hamburg, Germany.

Russia's account of the discussions on the topic was quite different.

According to Russia's Interfax news agency, Russian Foreign Minister Sergey Lavrov said Trump acknowledged that an anti-Russian campaign in the US was "looking odd" and that he accepted Putin's past statements denying Russia had any involvement in the 2016 election. A White House official pushed back, telling NBC News that Lavrov's characterization was "not accurate."

A day earlier, during a press conference alongside Polish President Andrzej Duda, Trump said Russia "could very well have" interfered in the election, but added that it "could have been a lot of people" as well.

Asked by NBC's Hallie Jackson if he could "definitively say that Russia interfered" in the 2016 presidential election, which multiple US intelligence agencies have concluded, Trump said he thought it was Russia but that "it could have been other people in other countries."

"I've said it very simply," Trump said. "I think it could very well have been Russia. But I think it could well have been other countries. I won't be specific. But I think a lot of people interfere. I think it's been happening for a long time. It's been happening for many, many years."

He also took the opportunity to blast his predecessor, President Barack Obama, for doing "nothing about it" after finding out about the intelligence community's conclusions in August.

"They say he choked," Trump said. "I don't think he choked. I think what happens is he thought Hillary Clinton was going to win the election and he said let's not do anything about it. Had he thought the other way, he would have done something about it."

Trump also compared the intelligence communities assessments with claims that Iraq had weapons of mass destruction espoused before the US got involved in the Iraq War.

"How everybody was 100% sure that Iraq had weapons of mass destruction," he said, "guess what — that led to one big mess. They were wrong. It led to a mess. So it was Russia, and I think it was probably also others."

But in a speech in Warsaw, Poland, after that press conference, Trump called on Russia to cease "destabilizing" nations and discouraged the Kremlin from supporting the governments of Syria and Iran.

"Today, the West is also confronted by the powers that seek to test our will, undermine our confidence, and challenge our interests," he said. "To meet new forms of aggression, including propaganda, financial crimes, and cyberwarfare, we must adapt our alliance to compete effectively in new ways and on all new battlefields.

"We urge Russia to cease its destabilizing activities in Ukraine and elsewhere, and its support for hostile regimes — including Syria and Iran — and to instead join the community of responsible nations in our fight against common enemies and in defense of civilization itself," Trump continued.

Before his Friday meeting with Putin, which lasted nearly two hours longer than the scheduled 30 minutes, Trump told the Russian president at a photo spray that it was "an honor to be with you."

Subjects that both Tillerson and Lavrov said were discussed at the meeting included a cease-fire agreement in Syria and a working group between the two nations on cybersecurity.

Tillerson said Trump and Putin showed a "clear positive chemistry."