Trump made the brief remarks in front of reporters, at a conference table surrounded by top officials at the start of a "working lunch" that began after he and Putin met behind closed doors for two hours with only their interpreters.

Trump sat down with Putin for a long-awaited summit, saying he wanted good relations with Russia, after blaming Washington's own past "foolishness and stupidity" for the countries' hostile ties.

"I've been saying, and I'm sure you've heard over the years ... that getting along with Russia is a good thing, not a bad thing," Trump said on Monday, seated next to Putin at the start of talks on Monday in an ornate presidential palace in neutral Finland.

Putin said it was time to talk about relations between Moscow and Washington and he suggested they should discuss difficult multinational issues.

"There are enough of them for us to start paying attention," he said.

Trump reached out to shake Putin's hand before the media were ushered out.

The two men were to meet alone apart from interpreters before a working lunch with aides. Trump said they would talk about a range of subjects, listing trade, the military, nuclear weapons and China.

But in his public remarks at the outset, he mentioned none of the issues that have lately brought US-Russian relations to the lowest point since the Cold War: Moscow's annexation of territory from Ukraine, its support for Syria's Bashar al-Assad, as well as Western accusations that it poisoned a spy in England and meddled in the 2016 US election.

Trump saved his public criticism for his own country, tweeting before the summit: "Our relationship with Russia has NEVER been worse thanks to many years of U.S. foolishness and stupidity and now, the Rigged Witch Hunt!"

The Russian foreign ministry "liked" his tweet.

Australian Associated Press