Donald Trump and Vladimir Putin are holding their first face-to-face talks, on the sidelines of the G20 summit in the German city of Hamburg.
“It’s an honour to be with you,” Mr Trump told Mr Putin, who responded: “I’m delighted to meet you personally.”
The US and Russian leaders say they want to repair ties damaged by crises including Russia’s alleged meddling in the US election.
Climate change and trade are set to dominate the two-day G20 meeting.
Violent clashes between protesters and police are taking place in the streets outside the venue, with dozens left injured.
A huge police operation is trying to keep demonstrators – who are protesting against the presence of Mr Trump and Mr Putin, climate change and global wealth inequalities – well away from the summit venue, and water cannon have been deployed.
US First Lady Melania Trump has been unable to leave her hotel in Hamburg because of the protests.
“Putin and I have been discussing various things, and I think it’s going very well,” Mr Trump told reporters while sitting alongside Mr Putin at the start of the talks, which were open to the media.
“We’ve had some very, very good talks. We’re going to have a talk now and obviously that will continue. We look forward to a lot of very positive things happening for Russia, for the United States and for everybody concerned.”
Mr Putin, via a translator, said that while they had spoken by phone, a phone conversation was never as good as meeting face to face.
Both men ignored shouted questions from reporters as the meeting went into private session.
Earlier, a brief video clip posted on the German government’s Facebook pageshowed the two men meeting for the first time and shaking hands, with Mr Trump patting Mr Putin’s arm as they smiled in the company of other leaders.
The two men have staked out opposing views on major international issues in the run-up to the summit:
- On Thursday, Mr Trump used a speech in the Polish capital Warsaw to call on Russia to stop “destabilising” Ukraine and other countries, and “join the community of responsible nations”
- Setting out his own G20 agenda in German financial newspaper Handelsblatt, Mr Putin called for US-led sanctions, imposed in response to Russia’s annexation of Crimea in 2014, to be lifted on his country
- Mr Putin also argued strongly in favour of the Paris climate agreement, saying it was a “secure basis for long-term climate regulation” and Russia wanted to make a “comprehensive contribution to its implementation”. President Trump has taken America out of the agreement.
Mr Trump’s choice of words aimed at Russia in his Warsaw speech suggests he recognises the political danger of being seen as too close to Mr Putin, the BBC’s diplomatic correspondent James Robbins says.
Russian media have low expectations of the meeting with one observer, Fyodor Lukyanov, writing in Rossiyskaya Gazeta: “The main thing is that nothing gets worse.”
The G20 (Group of Twenty) is a summit for 19 countries, both developed and developing, plus the EU.
In her summit opening statement, German Chancellor Angela Merkel said: “We are all aware of the great global challenges.
“We know that time is short and therefore solutions very often can only be found if we are ready to compromise and work together without bending over backwards too much because, of course, we can express different views on some issues.”
Canadian Prime Minister Justin Trudeau has urged G20 leaders to impress upon Mr Trump that he should act as a role model in addressing climate change.
“We’ll tell him it’s important to take a lead role in tackling climate change and creating good jobs,” he told German tabloid Bild, according to Reuters news agency.
Mrs Merkel has said the G20 will focus on the Paris climate deal but, as the G20 host, she will work to find compromises.
Mrs Merkel and other EU leaders have also expressed their commitment to an open international trading system, while the Trump administration pursues protectionism under the “America First” motto.
On Friday, Mrs Trump had been due to take part in an excursion with other leaders’ spouses, but her spokeswoman Stephanie Grisham said: “The Hamburg police could not give us clearance to leave.”