Putin said he is glad to meet his U.S. counterpart and wants to discuss with him relations between the two countries and global problems.
Putin said the talks were "open and business-like" and said, "I think we can call it a success". His 2016 opponent Hillary Clinton tweeted: "Great World Cup".
Finland has also been the site of previous US-Russia summits.
Trump kicked off his visit by posted on Twitter that the relationship between the USA and Russian Federation has "never been worse".
Peter Strzok is the former FBI agent whose anti-Trump text messages have prompted congressional investigations into political bias at the FBI.
Trump tweeted: "Our relationship with Russia has NEVER been worse thanks to many years of US foolishness and stupidity and now, the Rigged Witch Hunt!", referring to the current investigation by the special counsel into Russian meddling in the 2016 election. The Russian president touched down just after 1pm (1300 BST) local time, even though the official greeting with Trump at the Finnish presidential palace had been scheduled for 1.10pm.
Putin also addressed the issue of "so-called interference", saying he "had to repeat that the Russian state never interfered, and does not plan to interfere in internal American electoral process".
Putin and Trump are due to participate in one-on-one talks and a working lunch before attending a joint press conference.
Putin summit brings end to frosty US-Russia relations
Trump thought Putin had an "interesting idea" when he proposed a joint investigation Russian meddling . Anderson Cooper has never been one to hold back when it comes to critiquing President Donald Trump .
"That's what one of the purposes of this meeting is, so the president can see eye-to-eye with President Putin and ask him about it", Bolton said.
The president again congratulated Putin on the country's "spectacular" hosting of the World Cup.
The reason for Putin's delay was not clear.
The fresh indictments prompted a number of US senators, all but one Democrats, to request Trump cancel his summit with Putin.
Russia's new ambassador to Finland Pavel Kuznetsov, background righ escorts Russian President Vladimir Putin as he disembarks the plane at Helsinki airport in Vantaa, Finland, Monday, July 16, 2018. He said the leaders would discuss trade, nuclear issues and China.
Before the meeting, the president repeated his claim that Barack Obama had failed to act over the Russian attack.
The summit would cover nuclear disarmament, said Trump, who has bridled at the rapid expansion and modernization by Putin of Russia's nuclear arsenal. He told CBS News that he didn't "expect anything" from Putin, while his national security adviser said the US wasn't looking for any "concrete deliverables".
The United States has no extradition treaty with Moscow and can't compel Russian Federation to hand over citizens, and a provision in Russia's constitution prohibits extraditing its citizens to foreign countries.
Asked to explain why he would describe the E.U.as a foe, considering many of its nations are US allies, Trump backtracked slightly.
Trump has said he will raise the election meddling but does not expect to get anywhere. Although Finland is not a member of the alliance, it does cooperate on peacekeeping, training and security missions. North Atlantic Treaty Organisation has never been more together.