Video report by ITV News Europe Editor James Mates
Vladimir Putin has denied Russia interfered in the 2016 US elections, with Donald Trump repeating denials of collusion between his campaign and the Kremlin.
The Russian leader said there was "no evidence" of a conspiracy, a viewpoint he reiterated during talks between the two heads of state in Helsinki on Monday.
Mr Trump said that he raised the topic during the two-hour summit,but warned the divisive issue and subsequent Mueller investigation had soured relations between the US and Russia.
He conceded that the FBI advised him Russia was guilty of hacking, but appeared to side with the Russian leader's denial.
"President Putin says it's not Russia. I don't see any reason why it should be," Mr Trump said, adding that he "was extremely strong and powerful in his denial".
The comments came as the pair were repeatedly probed by reporters about alleged meddling in a follow-up press conference.
A defiant Mr Putin said: "I had to repeat that the Russian state never interfered, and does not plan to interfere in internal American electoral process."
Russia offers joint probe into allege meddling
In an apparent sign of co-operation, Mr Putin said Russia would be willing to conduct a joint investigation with the US into the alleged election meddling.
Last week, 12 Russian intelligence officers were indicted by the Mueller investigation on hacking charges.
They are accused of hacking into the computer networks of the Democratic National Committee and the presidential campaign of Mrs Clinton, stealing information on 500,000 US voters.
Mr Putin said that US officials could request Moscow to interrogate the group, and allow American counterparts to be present.
But he tempered that any favour would have to be returned by the US in the case of Bill Browder, a British investor charged with financial crimes in Russia.
Mr Trump himself rubbished the Mueller investigation, describing it as a "disaster".
"I think that the probe is a disaster for our country. I think it's kept us apart, it's kept us separated," he said.
"There was no collusion at all. Everybody knows it, people are being brought out to the fore.
"So far that I know virtually none of it related to the campaign. And they're going to have to try really hard to find somebody that did relate to the campaign, that was a clean campaign."
'Extraordinary' press conference impacting world order
ITV News Europe Editor James Mates described the press conference as "extraordinary", saying that it was already having ramifications across Europe and back home in the US.
Mates said that the FBI had been "dumped on" by Mr Trump after he decided to side with Mr Putin over their intelligence, something which would upset both Democrats and Republicans.
He added that Mr Trump's warming to Mr Putin has led some European nations to believe they can no longer trust the US.
"The German Foreign Minister said today that they can no longer rely upon the White House," he said.
"If you consider that this has been absolutely central to German foreign policy since the war, and that these views are being shared elsewhere in Europe as well, then you can see what a dramatic impact this week is making to transatlantic relations and to the world order."
Russia 'doesn't have dirt' on Trump
Reporters were answered with smiles and denials when Mr Putin was asked whether the Kremlin had collected compromising material on Mr Trump.
Moscow has been accused of gathering information on the US leader during a visit to Russia which could be used to blackmail him.
But Mr Putin rejected the allegations, describing them as "sheer nonsense".
Putin said he hadn't been aware of Mr Trump's visit to Moscow, before his 2016 election, and scoffed at the notion that Russian security services try to gather incriminating materials on businessmen.
He said: "Do you really believe that we try to shadow every businessman?"
'US-Russia relations set to improve'
Mr Trump admitted that ties between the US and Russia had been at one of their lowest points for years.
But the US leader said a productive dialogue between America and Russia was good for both countries and "is good for the world".
He told reporters the pair had discussed disagreements between their countries "at length", including the status of annexed Crimea.
Mr Trump added, however, that he believed relations between the two "changed as of about four hours ago".
He predicted the two leaders would meet often in the future.
Agreement on nuclear arms control
Mr Putin said he and Mr Trump have agreed to continue detailed discussions on arms control issues.
The Russian leader said Russia and the US should discuss a possible extension of the 2010 New START nuclear arms reduction treaty and the implementation of the 1987 Intermediate Nuclear Forces Treaty.
Mr Putin added that other issues that Russia would like to discuss in the arms control sphere are the US missile defence plans and the weaponisation of space.
On the question of nuclear tensions on the Korean peninsula, Mr Putin praised the US leader over efforts to resolve difficulties with North Korea.
'One of the best' World Cups
In a more light-hearted moment, Mr Putin gifted his American counterpart a football from the World Cup in Russia, which concluded on Sunday.
Handing Mr Trump the ball, the Russian joked "the ball is now in your court".
Mr Trump congratulated Russia holding a successful tournament, adding that it had been "one of the best".
He said that he would give the ball to his son, Barron, before chucking the ball at his wife Melania who sat in the front row.
Protester disrupts proceedings
Before the press conference had even begun, a protester caused a stir by holding up a placard.
Sitting among the reporters, the man, who identified himself as being a reporter from The Nation, brandished a sign which read: "Nuclear weapons ban treaty".
He was quickly bundled away by security before the two leaders appeared.