The US President robustly raised allegations that the Russians hacked last year’s election, according to secretary of state Rex Tillerson.
Mr Putin rejected the charges.
Officials said they also disagreed over North Korea – but they did agree to a new ceasefire in southwest Syria that will see the US, Russia and Jordan end hostilities and allow humanitarian access.
Their much-anticipated meeting, on the fringes of the G20 summit in Hamburg, was more than an hour and a half longer than scheduled.
Donald Trump may have made progress with Russia but with the rest of the G20 America has been at odds on one issue after another.
He does not see eye to eye with other leaders on climate change, immigration and most of all trade.
And it is on trade where there are deepest differences.
By mid-afternoon German Chancellor Angela Merkel was clearly concerned about the lack of progress on reaching the wording on the issue for the summit’s final communique.
In unusually frank language for this stage in a summit, she said discussions were proving very difficult.
But it was Mr Trump’s first meeting with President Putin – and the body language of their first handshake – that grabbed most headlines.
He was under pressure from politicians at home to confront his counterpart over the allegations of election meddling.
His administration is embroiled in investigations into whether his team colluded with the Russians to help him beat Hillary Clinton.
Mr Trump said earlier this week that Russia was probably involved, but that other countries could have also played a part.
Rex Tillerson described the Putin-Trump meeting as “robust and lengthy”.
“The President pressed President Putin on more than one occasion regarding Russian involvement,” he said.
“President Putin denied such involvement, as I think he has in the past.”
Russia foreign minister Sergei Lavrov, who was also present at the meeting, said Mr Trump had accepted his counterpart’s assurances.
However, Rex Tillerson said Russia had asked for “proof and evidence” of its involvement.
He added that the two men had “connected very quickly” and that there was “a very clear positive chemistry”.
The former Exxon Mobil boss has done business in Russia and is one of the only senior members of Mr Trump’s administration who has experience of dealing with Mr Putin.
This year’s G20 has all the appearances of previous summits. The motorcades, the family photos, the glitzy nights out and even the protests outside the summit – with more than 160 police officers injured.
But in reality it has been very different. In the past America has led at these gatherings, forcing the pace.
Donald Trump is sceptical about the basic principles of multilateral cooperation.
The concept of everyone winning by working together is alien to his transactional view of the world.
Under his presidency, America is retreating from leading the post-war world order.
And at this summit the US has been out of step with other G20 members. Some have called it G19 plus 1: America against the rest.
The G20 has been turned on its head.