Donald Trump and Vladimir Putin have held 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.”
Both sides listed a wide range of topics discussed, 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 have taken 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.
Earlier, US First Lady Melania Trump was 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.
Speaking afterwards, Mr Putin said: “I’ve had a very long conversation with the US president. We had a lot of issues to discuss, including Ukraine, Syria, and other problems, also some bilateral issues.
“We have again returned to the fight against terror and to cyber security.”
Secretary of State Rex Tillerson largely confirmed these were the topics covered, saying the leaders connected quickly and had positive chemistry.
But the two sides seem unable to agree on the exact outcome of talks over the Russian hacking allegations.
Russian Foreign Minister Sergei Lavrov said Mr Trump accepted Mr Putin’s assertions that they were not true.
Mr Tillerson, meanwhile, said the two men had had a “robust” discussion on the issue during the two hour and 15 minute meeting, and that Mr Trump had pressed the Russian leader on several occasions.
However, he said it was not clear whether the two countries would ever come to an agreement on what happened.
“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, according to the Associated Press news agency.
Mr Tillerson also said they had discussed Syria and its future, and shared “commonalities on what outcome should be”, although they had different ideas on how to get there.
They have, however, agreed to declare a ceasefire in south-west Syria from Sunday, Mr Lavrov said.
Earlier, a brief video clip posted on the German government’s Facebook page showed Mr Trump and Mr Putin 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.
Plenty to talk about, by the BBC’s Sarah Rainsford
The words were warm enough, but the body language was restrained as this meeting began. Neither man was smiling much as both said they hoped for positive results from their encounter. Their handshake, when it finally came, was brief and businesslike.
But they clearly had plenty to talk about, as their meeting went on well over the time allocated. Russia sees that alone as a success, proof that Vladimir Putin is a global leader to be reckoned with. No-one here is expecting any big deals though, like lifting sanctions for example.
The Kremlin has stressed all along that its main aim is to establish a “working dialogue” with Donald Trump, and perhaps begin the slow process of restoring relations with the US, which are at their lowest point in many years.
The two men 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 on his country, imposed in response to Russia’s annexation of Crimea in 2014, to be lifted
- 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 the US out of the Paris agreement
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, the US first lady 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.”
Mrs Trump herself tweeted concern for those injured in the protests.