"We were not able to clear all the backlog, but I think we made a first important step in this direction", he said.
"It's amusing to recall the nonsense from Obama et al about Russia being a weak "regional power", Alexey Pushkov, a member of the upper house of the Russian parliament, referring to former U.S. President Barack Obama.
Yet Trump appeared to take Putin's word in dismissing that conclusion.
Hannity also revisited a question that came up during the news conference - whether or not the Russians had compomising information on him. The media may not be the "enemy of the people" Trump says they are, but many are implacable enemies of this president.
"Russia has done nothing to deserve us meeting them in this way", said Nina Jankowicz, a global fellow at the Wilson Center's Kennan Institute who specialises in Russia, Ukraine and disinformation.
As one of our loyal readers, we ask you to be our partner. Staring intently at the correspondent, who he referred to as "distinguished colleague", Putin said, "It's hard to imagine an utter nonsense of a bigger scale than this".
U.S. intelligence officers concluded, in 2016, that Russian Federation authorised cyber attacks and fake news stories on social media which aimed to increase the chances of Mr Trump getting elected.
Chuck Hagel, a former senator and defense secretary, said that Trump "failed America" in the press conference.
Current and former Trump White House and campaign officials describe the president as obsessed by any suggestion that his elevation to the White House came as anything other than the product of his own hard work.
The conservative radio voice said he did not know whether to laugh or be angry at the "embarrassingly shallow and puerile, infantile questions" asked of President Donald Trump and Russian President Vladimir Putin on Monday in Helsinki, Finland.
"However, I also recognize that in order to build a brighter future, we can not exclusively focus on the past - as the world's two largest nuclear powers, we must get along".
First District Democratic Representative Chellie Pingree says the summit was "shameful", with Trump downplaying Russian attempts to influence USA elections just days after a dozen Russian intelligence agents were indicted for those attempts.
The Russian Foreign Ministry rejected last week's indictment as part of a "shameful comedy" they claim has been staged to prevent the normalization of Russia-U.S. ties.
Tensions have been brewing since the U.S Intelligence Community declared Russian Federation tried to meddle with the results of the 2016 United States elections.
"I was an intelligence officer myself and know how these dossiers are put together", said Putin.
"Would you now, with the whole world watching, tell President Putin, would you denounce what happened in 2016, and would you warn him to never do it again?"
He added: "I thought President Putin was very, very strong". We're doing well with North Korea, we have time. "There's no rush, it has been going on for many years".
Trump also discussed Federal Bureau of Investigation agent Peter Strzok's testimony before House lawmakers last week, calling him a "total phony".
His comments in Helsinki have sparked such anger in America that the United States political elite is likely to view any attempt by the Trump administration to mend fences with Moscow with the deepest suspicion.
House Speaker Paul Ryan, a fellow Republican, was openly critical of the president's assessment of Russia's conduct: "There is no question that Russian Federation interfered in our election and continues attempts to undermine democracy here and around the world".
'He's a disgrace to our country.
Strzok is on paid leave from the Federal Bureau of Investigation.