Neither leader revealed what was discussed.
The US President had raged at the Russian that it was "outrageous" of him to air the video which showed nuclear missiles raining down on the state of Florida.
CNN host Anderson Cooper has a more blunt assessment of Trump's comments: "You've been watching perhaps the most disgraceful performances by an American president in front of a Russian leader that I've ever seen".
"I don't see any reason why it would be" Russian Federation who interfered in our election, Trump told reporters gathered following a one-on-one meeting with Trump at a summit in Helsinki, Finland. "But I think we will end up having an extraordinary relationship".
"I'm not going in with high expectations but we may come out with some very surprising things", Trump said during his United Kingdom news conference. "I think the European Union is a foe, what they do to us in trade", he said. The Russians said it lasted two hours and 10 minutes.
While Trump was seen as hopeful about the meeting's outcome, Putin talked about the "problem areas of the world".
"Frankly, we have not been getting along for the last number of years".
Ari Fleischer, a Republican and prominent Trump defender who served as former President George W. Bush's press secretary, said that while he still does not believe Mr. Trump colluded with Russian Federation in the 2016 elections, he understands now why people think he's being blackmailed.
More protests followed Trump to Finland on Monday, ahead of his meeting with Putin. He nodded along to some of Trump's remarks before they were translated, showcasing his fluency in English. First, Hillary Clinton mocked Trump over playing for the Russians and then, Vlad made a decision to keep Donny waiting! Mr Putin took a ride in it from one building inside the Kremlin to another on his inauguration day in May.
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Palin says she sat through what she called a long interview full of "Hollywoodism's disrespect and sarcasm" before she walked out. That was a fun time, right? She claimed she had been approached to participate in a "legit opportunity" to honor "American vets".
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China chose to retaliate against the USA instead of addressing US concerns with China's unfair trade practices, according to USTR. A group representing global automakers warned last month Trump's tariff plans could cost hundreds of thousands of jobs.
With that, the two leaders gave a quick handshake and their private meeting in the opulent Gothic Hall was under way. "It will be determined by the heads of state themselves as they go along".
There was a lot up in the air going into Monday's talks, but the ongoing Russian Federation investigation loomed front and center.
"Most importantly we have a lot of good things to talk about", he said.
The Russian foreign ministry "liked" his tweet, and tweeted back: "We agree".
The meeting, in Helsinki, Finland, is the first stand-alone summit between the two leaders.
Trump and his wife Melania returned to their hotel after the breakfast and were expected to remain there for a few hours. Putin has been late for past meetings with the pope and British queen, among many others.
Trump and his aides have repeatedly tried to lower expectations about what the summit will achieve.
The fresh indictments prompted a number of US senators, all but one Democrats, to request Trump cancel his summit with Putin.
Trump's conciliatory tone towards Putin is a stark contrast to his combative attitude at last week's North Atlantic Treaty Organisation summit, highlighting once again the president's transactional approach to foreign policy.