"I respect the leaders of those (European) countries", Trump said. His 2016 opponent Hillary Clinton tweeted: "Great World Cup".
The leaders also met past year during a summit in Vietnam. In his brief comments, Putin said he wanted to make progress on some of the irritants in the U.S. -Russia relationship.
The president branded the special counsel investigation into Russia's election interference the "Rigged Witch Hunt".
"Our relationship with Russian Federation has NEVER been worse thanks to many years of US foolishness and stupidity", he said, "and now, the Rigged Witch Hunt!"
In response, Mrs May's spokesman said: "We have said before that it is important we engage in constructive dialogue to find the right way forward when it comes to the disagreement now taking place on tariffs".
Putin and Trump are due to participate in one-on-one talks and a working lunch before attending a joint press conference.
In his tweet, Trump said that the hacking of the servers took place during the Obama Administration.
Google fined $5 billion by European Union over Android
That would significantly open Android up to more competition, and possibly reduce Google's advertising revenues. The Android case decision comes after a three-year investigation into Google's mobile operating system.
Putin also handed Trump a soccer ball, in honor of Russia's successful hosting of the World Cup tournament this year and the United States picking up hosting duties in 2026.
The reason for Putin's delay was not clear.
After their "personal" talks, Putin and Trump will then each be joined by their top team of aides before giving another press conference.
US President Donald Trump on Monday met his Finnish counterpart Sauli Niinisto for breakfast here, just hours ahead of his first official summit with Russia's Vladimir Putin. Putin said before Trump spoke that Moscow never interfered and will never interfere in the American electoral process.
Earlier, Putin said the United States and Russian Federation should work jointly on cybersecurity. "We can do more, so if you want to do an arms race you'll lose", according to the report.
Yesterday Trump flew to Finland, the final stop on a weeklong trip that began last Tuesday.
But in advance of the high-stakes summit - where many observers say Putin has scored a win just by showing up - Trump's reputation has been getting a makeover. Although Finland is not a member of the alliance, it does cooperate on peacekeeping, training and security missions. "But, in a trade sense, they've really taken advantage of us and many of those countries are in North Atlantic Treaty Organisation and they weren't paying their bills". We'll be talking a little bit about China.
"I think the probe is a disaster for our country", Trump said.