"Getting along with Russian Federation is a good thing, not a bad thing", Trump told Putin during a handshake photo opportunity at their summit in Helsinki.
The summit began just hours after Trump blamed the United States - and not Russian election meddling or its annexation of Crimea - for a low-point in U.S. -Russia relations.
Putin spoke of the importance of the two countries working together and praised Trump, at one point interrupting the news conference to give the U.S. president a soccer ball.
After sitting down with Putin, Trump said relations had warmed - and Putin agreed.
Before he arrived, Trump denounced the US news media as the "enemy of the people", despite constitutional protections for freedom of the press.
Putin pushed back against claims that his government interfered in the US election.
Trump said last week that he would raise the meddling issue again with Putin, but questions have been swirling about whether Trump will sharply and publicly rebuke his Russian counterpart for the interference that prompted a special investigation probe that Trump has repeatedly labeled a "witch hunt".
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He again described Justice Department special counsel Robert Mueller's ongoing investigation as a "witch hunt" that has hampered USA relations with Russian Federation.
The summit with Putin is set to happen on Monday in Helsinki, Finland.
Peskov said the Russian leader respects Trump's "America first" stance because Putin puts Russia first, but said the only way to make progress at the summit is if both sides are open to finding areas of mutual benefit. "I think the president has made it very clear he intends to approach this discussion from a position of strength". The United States does not have an extradition treaty with Russian Federation. Trump tweeted. "Much of our news media is indeed the enemy of the people and all the Dems know how to do is resist and obstruct!"
Sources confirmed that Putin later admitted it was his intention to break Trump by making him say there were five lights instead of four, though he added that a part of him was disappointed at how easy it was. Responding to a reporter's question after that meeting, Trump said the two had a "very, very good start for everybody".
Aides had warned before the meeting that it might not produce big "deliverables".
On Syria, Putin said the conditions were in place for effective co-operation between the United States and Russian Federation, whose military intervention in 2015 saved the Assad regime from collapse.
"You can't solve problems if you're not talking about them", said Jon Huntsman, the USA ambassador to Russian Federation, in a briefing before the meeting.
After the summit, Huntsman's daughter Abby - a Fox News host - was less charitable about the president's diplomatic efforts.