In a meeting that ran longer than either side had planned, US President Donald Trump and Russia's Vladimir Putin discussed alleged Russian meddling in the US election on Friday but agreed to focus on better ties rather than litigating the past.

Trump, a Republican who called it an "honor" to meet with the Russian president, drew swift criticism from Democrats at home, who accused him of dismissing US intelligence and giving Putin's denial, reiterated on Friday, of Russian interference too much weight.

Secretary of State Rex Tillerson told reporters at a summit of leaders of the Group of 20 major economies in Hamburg that Trump had "positive chemistry" with Putin during the meeting, which lasted some two hours and 15 minutes.

He opened their discussion by pressing Putin about "the concerns of the American people regarding Russian interference in the 2016 election" and had a robust exchange, Tillerson said.

The Russian president has denied any meddling in the US democratic process last year and Moscow has asked for proof that it took place. Foreign Minister Sergei Lavrov said Trump accepted Putin's assertions that the allegations, backed by US intelligence agencies, were false.

Tillerson said they both sought to move on.

"The presidents rightly focused on how do we move forward from what may be simply an intractable disagreement at this point," Tillerson said.

That explanation did not sit well with Democrats.

“Working to compromise the integrity of our election process cannot and should not be an area where ‘agree to disagree’ is an acceptable conclusion," said US Senate Democratic leader Chuck Schumer in a statement.

On Thursday in Poland Trump gave lukewarm support to the view that Moscow interfered in the 2016 US political process.

Trump promised a rapprochement with Moscow during his campaign but has been unable to deliver because his administration has been dogged by investigations into the allegations of Russian interference in the election and ties with his campaign.

Trump says his team did not collude with Russia.

Tillerson said they agreed to work on commitments of "non-interference in the affairs of the United States and our democratic process as well as those in other countries."

Andrew Weiss, a former National Security Council official responsible for Russia, said Trump had sent the wrong signal with upbeat body language and by not pushing Putin harder on alleged Russian interference in the US presidential election.

"The atmospherics were chummy," said Weiss, who is now at Washington's Carnegie Endowment for International Peace think tank in Washington. "The clear push from Trump to normalize U.S.-Russian relations was on display in the meeting."

"GOING VERY WELL"

The two leaders spent a lot of time discussing Syria, and after their meeting an agreement between the United States, Russia and Jordan on a ceasefire in southwestern Syria was announced.

The face-to-face encounter was one of the most eagerly anticipated meetings between two leaders in years.

Trump and Putin spoke through translators with their respective foreign ministers present for six minutes before reporters were allowed into the room for their statements. Afterwards the reporters were ushered out and the meeting continued.

"President Putin and I have been discussing various things, and I think it's going very well," Trump told reporters, sitting alongside the Russian leader.

"We've had some very, very good talks. ... We look forward to a lot of very positive things happening for Russia, for the United States and for everybody concerned. And it's an honor to be with you."

Putin, through a translator, said: "We spoke over the phone with you several times," adding: "A phone conversation is never enough."

"I am delighted to be able to meet you personally, Mr. President," he said, noting that he hoped the meeting would yield results.

Both men sat with legs splayed. Trump listened intently as Putin spoke.

The encounter went longer than expected, and first lady Melania Trump came in at one point to urge them to conclude, Tillerson said. The two men later joined other G20 leaders at a concert. Mrs Trump sat next to Putin at dinner.

Before the get-together, some feared the US president, a political novice whose team is still developing its Russia policy, would be less prepared for the talks than Putin, a former KGB agent who has dealt with previous US presidents and scores of other world leaders.

Amid criticism of Russia's actions in Ukraine and Syria and the investigations into its role in the US campaign, Trump has come under growing pressure to take a hard line against the Kremlin.

On Thursday, Trump delivered some of his sharpest remarks about Moscow since becoming president, urging Russia to stop its "destabilizing activities" and end its support for Syria and Iran.

But Trump stopped short on Thursday of any personal criticism of Putin and declined to say definitively whether he believed US intelligence officials' assertion that Russia had interfered in the 2016 US election.

"I think it was Russia but I think it was probably other people and/or countries, and I see nothing wrong with that statement. Nobody really knows. Nobody really knows for sure,” Trump said on a visit to Poland.