President Donald Trump has said he wants another meeting with Russia’s Vladimir Putin to start implementing ideas they discussed in Helsinki.

He said the summit was a starting point for progress on a number of shared concerns.

Mr Trump accused the news media of trying to provoke a confrontation with Moscow that could lead to war, although concerns about the meeting have been raised by a broad cross-section of Republicans and Democrats.

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Donald Trump, left, tosses a football to first lady Melania Trump after Russian President Vladimir Putin presented it to him (Pablo Martinez Monsivais/AP)

Mr Trump tweeted a list of topics discussed at the summit, including terrorism, security for Israel, Middle East peace, Ukraine, North Korea and more, and wrote: “There are many answers, some easy and some hard, to these problems… but they can all be solved!”

“I look forward to our second meeting so that we can start implementing some of the many things discussed,” he wrote.

Mr Trump also met with Mr Putin last year in Germany and Vietnam.

Despite bipartisan criticism, Mr Trump pointed blame at the media, tweeting: “The Fake News Media wants so badly to see a major confrontation with Russia, even a confrontation that could lead to war. They are pushing so recklessly hard and hate the fact that I’ll probably have a good relationship with Putin. We are doing much better than any other country!”

“The Summit with Russia was a great success, except with the real enemy of the people, the Fake News Media,” he tweeted.

Numerous politicians have criticised Mr Trump for his post-summit statements raising doubts about Russia’s interference in the 2016 US elections, and past and current intelligence community officials also differed with many of his statements.

Senator Lindsey Graham, a Republican, acknowledged that Mr Trump has had a “bad week” on Russia.

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Donald Trump shakes hand with Vladimir Putin (Alexander Zemlianichenko/AP)

“I think it’s imperative that he understand that he’s misjudging Putin,” Mr Graham told reporters.

“I don’t think he was prepared as well as he should have been.”

Mr Graham said Mr Trump was right to criticise previous administrations for their handling of Russia.

But he said Mr Trump “is not making the problem better, he’s making it worse”.

Thursday marked the third day of Mr Trump trying to manage the political fallout from his widely criticised performance at the summit meeting with Mr Putin in Finland.

Mr Putin, in his first public comments about the summit, told Russian diplomats that US-Russian relations are “in some ways worse than during the Cold War”, but that the meeting with Mr Trump allowed them to start on “the path to positive change”.

“We will see how things develop further,” Mr Putin said, evoking unnamed “forces” in the US trying to prevent any improvement in relations and “putting narrow party interests above the national interest”.

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Russian president Vladimir Putin speaking in Moscow (Sergei Karpukhin/AP)

Mr Trump had toughened his tone about Russia on Wednesday, saying in a CBS News interview that he told the Russian president to his face during Monday’s summit to stay out of America’s elections “and that’s the way it’s going to be”.

That rhetoric marked a turnabout from Mr Trump’s first, upbeat description of the meeting.

Mr Trump has refined and sharpened his presentation since Helsinki.

At the news conference with Mr Putin, he was asked if he would denounce what happened in 2016 and warn Mr Putin never to do it again, and he did not directly answer.

Instead, he delivered a rambling response, including demands for investigation of Hillary Clinton’s email server and his description of Mr Putin’s “extremely strong and powerful” denial of meddling.

Mr Trump asserted on Wednesday at the White House that no other American president has been as tough on Russia.