At a summit between the two leaders in Helsinki yesterday, Mr Trump said the Russian collusion investigation has been a “disaster” for the United States and has kept the two countries “separated”.
He reiterated there had been “no collusion” and that he ran a “clean campaign” and beat his Democratic presidential rival Hillary Clinton “easily”.
The American president said it is a “shame” there is a cloud over his administration, but said he ran a “brilliant campaign and that’s why I’m president”. Mr Putin said the “so-called Russian interference” was brought up by Mr Trump.
He said: “The Russian state never interfered, and does not plan to interfere in internal American electoral process.”
Mr Putin said of the collusion claims that there is “no evidence when it comes to the actual facts”. The Russian president made an “incredible offer” to allow Russian and US investigators to work together on allegations of Russian cyber attacks, Mr Trump said.
He added that Mr Putin suggested the US should provide its intelligence to the Russian military so Russia can determine the truth of what happened.
Mr Trump said he has “great confidence” in his intelligence agencies who have concluded Russia interfered in the election.
But the US president said Mr Putin was “incredibly strong and powerful today” in his contention that Russia had nothing to do with election interference.
The Russian president also rejected allegations that Moscow has collected compromising material on Mr Trump or his family.
Dismissing the claims as “sheer nonsense”, Mr Putin said he had not been aware of Mr Trump’s visit to Moscow a few years before his 2016 election.
The former KGB agent scoffed at the notion that the Russian security services try to gather incriminating materials on business figures, saying: “Do you really believe that we try to shadow every businessman?”
In general, the Russian leader said, the talks with Mr Trump took place in an “open and businesslike atmosphere” and he characterised them as “successful and useful”.
Mr Trump told the press conference that the US and Russia must find ways to “co-operate in pursuit of shared interests”. The US leader said a productive dialogue between America and Russia is good for both countries and “is good for the world”.
Mr Trump added they had discussed disagreements between their countries “at length”, and accepted that relations between them have never been worse.
However, Mr Trump added that he thinks “that changed as of about four hours ago”.
He said he is sure that he and Mr Putin will meet again often in the future.
Mr Trump confirmed that he addressed meddling by Russia in the 2016 US election with his Russian opposite number, but the US leader is not condemning Moscow’s conduct publicly.
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He said his message was “best delivered in person”, adding that he “spent a great deal of time” talking about election meddling.
Mr Putin feels strongly about the issue, Mr Trump claimed, and “has an interesting idea”.
The summit comes days after the US indictment of 12 alleged Russian military intelligence agents for sophisticated hacking in the 2016 election.
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.
The two leaders said they are exploring ways to protect Israel from conflict raging near its border in Syria.
There was no commitment to any specific actions, but both said that ensuring Israel’s security was a priority.
Israel is deeply concerned about Iran’s presence in Syria, where Iranian forces and proxies have been fighting on behalf of the Syrian government, which is also supported by Russia.
Israeli prime minister Benjamin Netanyahu has appealed to both Mr Trump and Mr Putin to eliminate the Iranian presence, which the Jewish state regards as an existential threat.
On the question of nuclear tensions on the Korean peninsula, Mr Putin praised the US leader over efforts to resolve difficulties with North Korea.
The Russian leader said: “It’s good that the gradual resolution of the problem of the Korean peninsula has begun.”
He continued, saying: “In many respects, this became possible due to the fact that President Trump personally got involved in the resolution, building dialogue in the spirit of co-operation, not confrontation.”
Mr Trump, when asked about a Russian gas pipeline to Germany, noted that the US and Russia compete in the energy market.
He said that when he referred to Mr Putin as a competitor, he meant it as a compliment. Mr Trump had previously criticised the pipeline.
An apparent protester was seated with the American press corps holding a sign about nuclear weapons. The man identified himself as a reporter from the liberal magazine The Nation and was escorted from the press conference by security.