The US President, speaking alongside Putin at a press conference in Helsinki, Finland, admitted that the relationship between the two countries 'has never been worse' but said 'that changed as of about four hours ago'.
His Russian counterpart denied meddling in the 2016 presidential election but admitted he had hoped Trump would win, saying: 'I wanted him to win because he talked about normalising Russian-American relations.'
Trump backed up Putin's denials, saying he thought Russia had no reason to interfere in the election and contradicting the FBI which believes Moscow was responsible for hacking during the campaign.
He said that 'we've all been foolish... we've both made mistakes' and that today's summit at the Finnish Presidential Palace was the beginning of a process of restoring ties.
'It is in the interest of both of our countries to continue our conversation and we have agreed to do so,' Trump said, having earlier shot a wink at the Kremlin strongman ahead of their private talks.
In a lighthearted moment, Putin gave Trump a ball from the 2018 World Cup, to symbolise North America hosting the tournament in 2026, saying: 'Now the ball is in your court'.
Trump, who praised Russia's hosting of the World Cup, said his son would like the gift and threw it into the audience, where his wife Melania caught it.