After the Helsinki summit, Trump was criticized at home for failing to publicly confront Putin over Moscow's meddling in the 2016 presidential election, and for seeming to contradict his own intelligence agencies on the threat from Russian Federation.
Trump has repeatedly denied his campaign colluded with Russian Federation and has characterized the investigation by Special Counsel Robert Mueller as a witch hunt.
Mr Putin said on Friday he is ready to travel to the USA under the right conditions and has invited Mr Trump to Moscow for a second meeting.
Trump has defended his conduct in a two-hour private meeting with Putin and at a joint news conference.
Putin had said earlier Friday during a meeting in Johannesburg, South Africa, that he was ready to invite Trump and also ready to visit Washington if conditions are right.More news: UK's Brexit negotiating position a 'far advanced offer' - Raab
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We are ready to invite President Trump to Moscow. "He has this invitation already and I told him about it", according to CNN. Collins asked. "Mr. President, are you anxious about what Michael Cohen is going to say to prosecutors?.Why has Vladimir Putin not accepted your invitation, Mr. President?"
The statement comes as Trump's apparent eagerness to embrace Putin is coming under increasing scrutiny after the summit between the two leaders last week in Helsinki. The White House called Collins' questions "rude".
A summit last week between the pair in Helsinki caused Trump serious domestic problems, with the U.S. president accused of appeasing a man who allegedly tried to tilt the 2016 USA presidential election. He later said he had misspoken at the summit.
On Friday afternoon, Trump will convene a National Security Council meeting devoted to the issue of election security.
By saying that he's willing to go to Washington if conditions are "appropriate", Putin underlines that stance and effectively puts pressure on Trump to try to stamp out opposition.
He did not clarify if that was a face-to-face invitation to be followed by a formal one.