After months of anticipation and intrigue, US President Donald Trump and Russian President Vladimir Putin sat down for their first meeting on the sidelines of the summit in the German city of Hamburg.

“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.”

Against a backdrop of violent anti-globalisation protests that have seen at least 160 police officers injured the leaders’ private meting ran well over time.

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.

US Secretary of State Rex Tillerson said he tried several times to remind President Donald Trump about the ticking clock during his meeting with Russian President Vladimir Putin.

“One of the reasons it took a long time … is because once they met and got acquainted with one another fairly quickly, there was so much to talk about. There was just such a level of engagement and exchange that neither of them wanted to stop,” Tillerson told reporters.

He said the two men connected quickly and had “a very clear positive chemistry.”

“Several times I had to remind the president. People were sticking their heads in the door. They even … sent the first lady at one point to see if they could get us out of there. But it didn’t work,” Tillerson said.

“We went another hour after she came in to see us. Clearly she failed,” he added.

In their meeting, Mr Trump raised concerns about Moscow’s meddling in the 2016 presidential election, Mr 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.

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.

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.”

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 160 police officers were injured in clashes with protesters, who were torching cars, barricades and rubbish bins in protests against capitalism and globalisation.

Cars burn on the streets of Hamburg as German police fought to control wild demonstrations.

German host Chancellor Angela 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.

US first lady Melania Trump was kept from joining the other spouses of leaders at the summit for their own program of events when Hamburg police did not clear her to leave the government guest house where she and Mr Trump spent the night because of the protesters which included a tour of the city’s historic harbour.

Police forces around Germany dispatched reinforcements to help 15,000 police already deployed to the northern port city for the G20 summit as the violence escalated. At least 15 people were arrested and dozens more held for questioning.

Police said violence that erupted during G20 marches on Thursday continued into Friday, with far-left protesters slashing the tires of a car belonging to Canada’s G20 delegation and smashing windows of the consulate of Mongolia.

G20 protesters fill the Hamburg night with flames.

Dozens of officers sealed off parts of Hamburg while water cannons were used to force back protesters across the city. None of the activists managed to push into the no-go zone around the summit that the police had established.

Activists took to the streets to protest globalisation, economic inequality and what they see as a lack of action on climate change.

-with wires and ABC