Donald Trump is embarking on his first foreign trip as president but will board Air Force One facing considerable domestic turbulence.

Mr Trump has in vain tried to put investigations into his campaign and his first four months in office behind him.

Amid claims about his campaign's relations with Russia and whether he tried to stop an FBI probe into the issue, Mr Trump claimed to be the most hounded president in history.

Asked if he had done anything that might merit prosecution or even impeachment, Mr Trump said "no" and then added of the lingering allegations and questions: "I think it's totally ridiculous. Everybody thinks so."

Mr Trump is leaving for his first foreign trip, to the Middle East and beyond, and aides had hoped the disarray at home would have been calmed if not resolved by take-off time.

Republicans on Capitol Hill hoped the same, reasoning the appointment of a special counsel could free them to work on a major tax overhaul and other matters without constant distractions.

Mr Trump said he was about to name a replacement for former FBI boss James Comey, another effort to settle the waters with former senator Joe Lieberman seen as the front-runner.

Mr Trump clearly knew what he wanted to say as he took a few questions at a news briefing with visiting Colombian President Juan Manuel Santos.

Asked if he urged Mr Comey at a February meeting to drop his probe of the Russia connections of Mr Trump's national security adviser, Michael Flynn, the president said: "No. No. Next question."

Did he collude with Russia in his campaign to defeat Democrat Hillary Clinton?

"Everybody, even my enemies, have said there is no collusion," he replied.

He added: "The entire thing has been a witch hunt.

"This is the single greatest witch hunt of a politician in American history!"

He said he respected the special counsel appointment but also said it "hurts our country terribly".

Across town, deputy attorney general Rod Rosenstein was briefing the Senate about his decision to appoint former FBI Director Robert Mueller to lead the independent Trump-Russia probe.

Senators said Mr Rosenstein steered clear of specifics while making clear Mr Mueller has wide latitude to pursue the investigation wherever it leads, potentially including criminal charges.

Despite the president's furious reaction, some fellow Republicans welcomed Mr Mueller's appointment and expressed hopes it would restore some composure to a capital plunged in chaos.

One striking piece of news emerged from Mr Rosenstein's briefing.

He told senators he had already known Mr Comey was getting fired even as he wrote the memo Mr Trump cited as a significant justification for the FBI director's dismissal.

Mr Trump himself had already contradicted that explanation, telling interviewers earlier he had already decided to dismiss Mr Comey.

He offered new justifications for his decision on Thursday, even while referring to the Rosenstein memo as "a very, very strong recommendation."

Mr Trump referred to Mr Comey's appearance at a recent Capitol Hill hearing, after which the Justice Department ended up having to amend part of his evidence regarding last year's probe of Hillary Clinton's email practices.

"That was a poor, poor performance," Mr Trump said.

"And then on top of that, after the Wednesday performance by Director Comey, you had a person come and have to readjust the record, which many people have never seen before, because there were misstatements made."

The Justice Department said Mr Mueller, the new special counsel, has been given sweeping power to investigate Russian interference in the 2016 presidential campaign, including potential links between Moscow and Trump associates.