US President Donald Trump and Russian President Vladimir Putin have met for the first time, shaking hands at G20 talks set amid a backdrop of violent anti-globalisation protests in Hamburg that saw at least 196 police officers injured.

Key points: The US and Russian leaders spoke for more than two hours

The US and Russian leaders spoke for more than two hours Donald Trump raised concerns about Moscow's alleged meddling in the 2016 presidential election

Donald Trump raised concerns about Moscow's alleged meddling in the 2016 presidential election Meeting comes amid violent protests in which 160 police officers were injured

After months of anticipation and intrigue, the presidents sat down for their first meeting on the sidelines of the summit in the German city, making brief remarks before a private meeting.

"We look forward to a lot of positive things happening, for Russia, for the United States and for everybody concerned," Mr Trump said, sitting next to Mr Putin.

"It's an honour to be with you."

The White House said in advance that 35 minutes had been allotted for the meeting. But it extended well beyond that, clocking in at two hours and 16 minutes, the State Department said.

In their meeting, Mr Trump raised concerns about Moscow's meddling in the 2016 presidential election, US Secretary of State Rex Tillerson said.

Mr Trump has avoided stating unequivocally in the past that Russia interfered, even as investigations proceed into whether his campaign colluded with Russians who sought to help him win.

"I think the President is rightly focused on how do we move forward from something that may be an intractable disagreement at this point," Mr Tillerson said.

Russian Foreign Minister Sergey Lavrov, who attended the meeting along with Mr Tillerson, said Mr Trump accepted Mr Putin's assurances that Russia did not meddle in the US election.

But Mr Tillerson said the Russians had asked for "proof and evidence" of its involvement. A day earlier, Mr Trump had said Russia probably meddled but that other countries likely did, too.

Speaking to reporters after the meeting, Mr Tillerson said the discussion about the election meddling was "robust and lengthy".

Mr Tillerson said the two leaders had agreed to continue the discussion, with an eye toward securing a commitment that Russia would not interfere in US affairs in the future.

In their meeting, the two also discussed a ceasefire deal for south-western Syria that was reached by Russia and the United States.

Vladimir Putin told reporters phone conversations with the US President were "never enough". ( AP: Evan Vucci )

Pair discussed 'various things'

Mr Trump himself offered no details about what issues he and the Russian leader had discussed, describing them only as "various things".

Mr Putin was similarly vague, telling reporters through a translator that they were discussing international problems and bilateral issues.

Sorry, this video has expired Donald Trump and world leaders arrive for the start of the G20 summit

Still, Mr Putin described the fact that they were meeting as a positive sign in itself, and he said he hoped the meeting would "yield positive results".

"Phone conversations are never enough definitely," Mr Putin said.

"If you want to have a positive outcome in bilaterals and be able to resolve most international policy issues, that will really need personal meetings."

Mr Trump also held his first face-to-face meeting since becoming President with his Mexican counterpart Enrique Pena Nieto, hailing him as his "friend" but insisting Mexico would "absolutely" pay for his proposed border wall.

Mr Putin was seen talking to G20 host German Chancellor Angela Merkel.

Sorry, this video has expired Angela Merkel speaks with Vladimir Putin

Ms Merkel said the priorities of the leaders' summit would be global trade and growth, climate change, energy, women's rights and development in Africa.

"We all know the great global challenges, and we know these are urgent matters, and therefore solutions can only be found if we look for compromises and work together," she said in opening the first meeting.

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Prime Minister Malcolm Turnbull, who is in Hamburg with Finance Minister Mathias Cormann, said he would talk about counter-terrorism measures, trade and energy security.

North Korea's intercontinental ballistic missile test was expected to feature heavily in discussions at the G20, and Mr Turnbull has called on China to lead efforts on curbing the rogue nation's nuclear ambitions.

Outside the summit venue, almost 200 police officers were injured in clashes with protesters, who were torching cars, barricades and rubbish bins in protests against capitalism and globalisation.

US first lady Melania Trump was kept from joining the other spouses of leaders at the summit for their own program of events, which included a tour of the city's historic harbour.

The first lady's spokesperson said Hamburg police had not cleared her to leave the government guest house where she and Mr Trump spent the night because of the protesters.

Sorry, this video has expired G20 protests continue in Hamburg

Reuters/AP