Separately, The Washington Post reported Friday that the FBI investigation into possible co-ordination between Russian Federation and the Trump presidential campaign was moving closer to the White House.
The probe marks a third line of inquiry regarding Russian influence, adding to a more general investigation into Russian meddling in the investigation, and a more specific investigation into Trump campaign ties to the country.
"There is no collusion between certainly myself and my campaign, but I can always speak for myself, and the Russians - zero", Trump told reporters.
In the briefing, Rosenstein acknowledged that he knew Trump was going to fire Comey before he wrote the memo, saying Trump approached him the day before to seek his "advice and input".
The Washington Post meanwhile said the Federal Bureau of Investigation has identified an unnamed senior White House official as a "significant person of interest" in its sprawling probe of Russian meddling in the 2016 presidential election.
"I just fired the head of the FBI He was insane, a real nut job", Trump said, according to official meeting notes which were read aloud to the New York Times by an administration source.
President Trump fired FBI Director James B. Comey on May 9.
"That's taken off", the president reportedly said.
During the meeting - in which Trump allegedly revealed classified information provided by Israel - the president reportedly said Comey's firing a day earlier had had relieved him of "great pressure" over his ties to Russian Federation. However the White House said there would be no announcement Friday. But the president undercut that argument a day later, telling NBC News, "When I chose to just do it, I said to myself - I said, you know, this Russian Federation thing with Trump and Russian Federation is a made-up story".More news: NKorea missile programme progressing faster than expected, says South
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The Washington Post reported that investigators have identified a current White House aide as a person of interest in the Russian Federation investigation.
The White House repeated its assertion that a "thorough investigation will confirm that there was no collusion between the campaign and any foreign entity". A Washington Post report, citing anonymous sources familiar with the matter, said a senior Trump adviser is now considered a person of interest in the law enforcement investigation into whether Trumps campaign associates co-ordinated with Russian Federation in an effort to sway the 2016 election.
Former FBI director James Comey, who was sacked by Donald Trump amid an agency probe into alleged Russian meddling in the United States election, has agreed to testify before the Senate Intelligence Committee at a public hearing. "I hope that former Director Comey's testimony will help answer some of the questions that have arisen since Director Comey was so suddenly dismissed by the President", Warner said.
The White House has struggled since Comeys firing to explain the chain of events that led to it and the Justice Departments involvement in that decision.
Mr Trump has insisted at times the decision was his alone, but he also has pointed to a "very strong" recommendation from Deputy Attorney-General Rod Rosenstein. But he added, "I wrote it".
The memo focused on Comey's handling of the Hillary Clinton email investigation, particularly the FBI director's decision to divulge details to the public at various junctures during her presidential campaign against Trump.
On Thursday, Mr Trump declared himself the victim of the "greatest witch hunt" in American political history and denied allegations of collusion.
Republicans have largely stood behind Trump in the first months of his presidency as the FBI and congressional investigations into Russia's election meddling intensified.