US President Donald Trump cast doubt on the conclusion of US intelligence agencies that Russia interfered in the 2016 presidential election, saying after his summit in Helsinki with Russian President Vladimir Putin that the autocrat gave him a "very powerful" denial.

After Putin said his Government played no role in trying to sabotage the US election, Trump offered no push-back and went on to condemn the Justice Department's investigation of Russian interference as "a disaster for our country."

Concluding their first formal one-one-one summit here today, Trump said his message regarding the Russian interference "was a message best delivered in person" during the meeting, during which the two leaders "spent a great deal of time" discussing the Kremlin's interference.

Putin insisted publicly that the "Russian state has never interfered and is not going to interfere in internal American affairs," and Trump declined to dispute his assertions, instead saying that Putin "has an interesting idea" about the issue of interference.

"I don't see any reason why" Russia would interfere in the election, Trump said as he stood next to Putin at a joint news conference after their talks in the Finnish capital ended. Of their private conversation in Helsinki about the interference, Trump said, "President Putin was extremely strong and powerful in his denial today."

Trump also insisted that "there was no collusion" between his campaign and Moscow. "I didn't know the President. There was nobody to collude with. There was no collusion with the campaign."

Trump said that he holds "both countries responsible" for the frayed relations between the two nations and attacked Special Counsel Robert Mueller's investigation.

Putin later confirmed that he did want Trump to win in 2016, "because he talked about normalising relations" between Russia and the United States. Yet he did not answer directly when pressed on whether the Russian Government had compromising information on Trump or his family members, dismissing it by saying that "it's hard to imagine greater nonsense." He told reporters, "Please throw this junk out of your head."

During their two-hour, one-on-one talks earlier, in which the leaders were accompanied only by interpreters, Trump and Putin discussed their disagreements "at length," Trump said. He added: "Our relationship has never been worse than it is now. However, that changed, as of about four hours ago."

The summit began hours after Trump, in a series of tweets, blamed his own country, rather than Russia, for the hostilities between their two nations.

Speaking first at the news conference, Putin said the talks took place "in a frank and businesslike atmosphere," adding: "I think we can call it a success." He said that although bilateral relations have been "going through a complicated stage," there was "no solid reason" for that. "The Cold War is a thing of the past," he said.

He added later that Trump "mentioned the so-called interference of Russia in the American election" in 2016. Putin again denied any involvement by the Russian state and said any evidence of interference can be analysed through a joint working group on cybersecurity.

Putin said later in response to a question that US investigators possibly could come to Russia to participate in the questioning of suspects after a dozen Russian intelligence officers were indicted in the United States on charges of election interference.

Elaborating, Putin said representatives of the Mueller probe could be present at interrogations of suspects in Russia - as long as Russians would be able to do the same at the questioning of US intelligence agents that Moscow suspects of carrying out crimes on Russian soil. Any questions about Russian interference in the US elections, he said, should be resolved by the courts and according to existing intergovernmental agreements.

"Let the Mueller commission send us a request, and we will do the work necessary to respond," Putin said. "We can expand this cooperation - but we will then also expect from the US side access to people who we believe are members of the intelligence agencies."

In response to questions, Trump subsequently said that both countries were to blame for the deterioration of relations. "I do feel that we have both made some mistakes," he said. He added that "there was no collusion" between his campaign and Russia, and he lamented that the special counsel's investigation into the matter has had an impact on US-Russian relations.

"I think the probe has been a disaster for our country," he said. "It's ridiculous what's going on with the probe."

Trump critics reacted harshly. Former CIA director John Brennan wrote in a tweet: "Donald Trump's press conference performance in Helsinki rises to & exceeds the threshold of 'high crimes & misdemeanors.' It was nothing short of treasonous. Not only were Trump's comments imbecilic, he is wholly in the pocket of Putin. Republican Patriots: Where are you???"

Senator Jeff Flake, (R), a frequent Trump critic on the Republican side, said: "I never thought I would see the day when our American President would stand on the stage with the Russian President and place blame on the United States for Russian aggression. This is shameful."

Senator Lindsey Graham, (R), tweeted: "Missed opportunity by President Trump to firmly hold Russia accountable for 2016 meddling and deliver a strong warning regarding future elections. This answer by President Trump will be seen by Russia as a sign of weakness and create far more problems than it solves."

Referring to a souvenir soccer ball that Putin handed Trump toward the end of the news conference, Graham added, "Finally, if it were me, I'd check the soccer ball for listening devices and never allow it in the White House."

Trump said before the closed-door meeting that he and Putin had a "lot of good things to talk about, and things to talk about," including trade, military issues, nuclear proliferation and China, in particular their "mutual friend," Chinese President Xi Jinping.

Trump did not mention Russia's interference in the 2016 presidential campaign as one of the topics to be discussed before the meeting began.

The meeting began later than originally planned, after the perennially tardy Putin arrived in Helsinki well behind schedule, keeping Trump waiting. The one-on-one meeting lasted about two hours, longer than anticipated. It was initially scheduled to take 90 minutes.

The two leaders then went into an expanded meeting that included top aides. At the start of it, Trump, responding to a shouted question from a reporter, said: "I think it's a good start. Very, very good start for everybody."

Although most US officials argue that Russia's interference in the 2016 US presidential election, use of a nerve agent on British soil and aggression in Ukraine and Syria have worsened relations, Trump instead faulted "US foolishness and stupidity" in tweets, as well as the expansive Justice Department investigation into Russia's election intrusion.

"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 Monday morning as he prepared for his meeting with Putin.

Trump is facing immense pressure to aggressively confront Putin over Russia's election interference, especially after the Justice Department indicted 12 Russian intelligence officials and charged them with hacking and stealing Democratic emails, as part of a broad subterfuge operation that US intelligence agencies believe was ordered by Putin to help elect Trump.

But Trump's comments today were in sync with the argument Putin and his Government have long made, which is that the policies of the Obama Administration - as well as the investigation into election interference, which Putin repeatedly has denied - inflamed tensions between the two nuclear superpowers.

The Russian Foreign Ministry's official Twitter account retweeted Trump's "US foolishness and stupidity" tweet and said, "We agree."

In another tweet, Trump sought to pin blame for the matter on Obama.

"President Obama thought that Crooked Hillary was going to win the election, so when he was informed by the FBI about Russian Meddling, he said it couldn't happen, was no big deal, & did NOTHING about it. When I won it became a big deal and the Rigged Witch Hunt headed by Strzok!" Trump wrote, referencing first 2016 Democratic presidential nominee Hillary Clinton and then FBI agent Peter Strzok, who testified before Congress in a combative hearing last week.

"Unfortunately, no matter how well I do at the Summit, if I was given the great city of Moscow as retribution for all of the sins and evils committed by Russia over the years, I would return to criticism that it wasn't good enough - that I should have gotten Saint Petersburg in addition!" Trump tweeted.

And after a week of denigrating the US news media on foreign soil, Trump continued in his tweetstorm: "Much of our news media is indeed the enemy of the people and all the Dems know how to do is resist and obstruct! This is why there is such hatred and dissension in our country - but at some point, it will heal!"

Putin's allies say that last weekend's indictments represented the latest effort by the Washington establishment to derail Trump's effort to improve relations with Russia.

"It seems to us the opponents of the improvement of US-Russia relations should not be allowed to endlessly exploit this harmful topic, which is being kept afloat artificially," Putin's foreign policy adviser Yuri Ushakov said ahead of the summit, according to Interfax.