HELSINKI — US President Donald Trump declared Monday that his summit with Russian counterpart Vladimir Putin had begun well, after they met one-on-one for two hours.

"Very good start," Trump said in response to reporters as the leaders were joined by senior officials for further discussions.

The two leaders began the historic summit vowing their determination to forge a reset of troubled relations between the world's greatest nuclear powers.

Trump, bent on forging a personal bond with the Kremlin chief despite allegations of Russian meddling in US politics, went into the summit blaming "stupidity" by his predecessors for plunging ties to their present low.

Looking sombre, the two leaders exchanged a few opening remarks in front of the press at the start of their summit.

Putin, basking in congratulations from Trump and other world leaders for the successful staging of the World Cup in Russia, said: "The time has come to talk in a substantive way about our relations and problem areas of the world."

Before the two leaders went into a first session between just themselves and their interpreters, Trump said the summit would cover "everything from trade to military to missiles to nuclear to China".

"Frankly, we have not been getting along for the last number of years. And I really think the world wants to see us get along. We are the two great nuclear powers," he said.

"I've not been here too long (as president), it's getting close to two years, but we'll be having an extraordinary relationship, I hope so."

Shortly before the summit opened, Trump was asked if he would press Putin over Russia's alleged manipulation of the 2016 election that brought the mercurial property tycoon to power. He said only: "We'll do just fine."

Many US critics had called for the summit's cancellation after new revelations surrounding the alleged election meddling.

But Trump has insisted it is "a good thing to meet", as he attempts to replicate with Putin the sort of personal rapport he proclaims with the autocratic leaders of China and North Korea.

If the pair do find common ground, the summit may take the heat out of some of the world's most dangerous conflicts, including Syria.

But there are many points of friction that could yet spoil Trump's hoped-for friendship with the former KGB spymaster.

Trump began the day by firing a Twitter broadside at his domestic opponents, blaming the diplomatic chill on the investigation into alleged Russian election meddling.

"Our relationship with Russia has NEVER been worse thanks to many years of US foolishness and stupidity and now, the Rigged Witch Hunt!" Trump tweeted.

Russia's foreign ministry tweeted in response: "We agree."

Trump's US opponents tried, in turn, to gain traction for the hashtag #BAF (Blame America First).

After a stormy NATO summit in Brussels last week, Trump was accused by critics of cozying up to Putin while undermining the transatlantic alliance.

But over breakfast with Finland's President Sauli Niinisto, he insisted NATO "has never been stronger" and "never been more together" thanks to his insistence on all allies paying their fair share.

Trump, a brash 72-year-old billionaire, has been president for 18 months while Putin, 65, has run Russia for the past 18 years. — Agencies