President Donald Trump has said the decision to appoint a special counsel to oversee the inquiry into Russian influence on his election is hurting America "terribly".
Speaking at a news conference in Washington, he denied any collusion with Russia during his election campaign last year.
"The entire thing has been a witch hunt and there is no collusion," he said.
Former FBI chief Robert Mueller has been selected to lead the inquiry.
Mr Mueller's appointment was welcomed by politicians from both sides.
Calls for a special investigation had mounted after Mr Trump fired FBI Director James Comey last week.
On Thursday, Mr Trump denied trying to influence the investigation by sacking Mr Comey.
"Director Comey was very unpopular with most people," he suggested.
"I actually thought when I made that decision... that it would be a bipartisan decision because you look at all of the people on the Democratic side, not only the Republican side, that were saying such terrible things about Director Comey."
On Wednesday, Mr Trump had said no politician in history "has been treated worse or more unfairly" than himself.
The announcement of a special counsel apparently took the White House by surprise, with Mr Trump only being informed of it after Deputy Attorney General Rod Rosenstein had signed the order.
The FBI and Congress are looking into potential links between Mr Trump's campaign team and Russia. Mr Mueller will take over the FBI investigation.
US intelligence agencies believe Moscow tried to tip November's presidential election in favour of Mr Trump.
Meanwhile, the New York Times reports that former Trump aide Michael Flynn told his transition team at the beginning of January - earlier than was previously thought - that he was under federal investigation for working as a paid lobbyist for Turkey during the election campaign.
Mr Trump appointed Mr Flynn as his national security adviser weeks later despite the warning, but he was sacked after just 24 days.
In his statement announcing Mr Mueller's appointment, Mr Rosenstein said: "The public interest requires me to place this investigation under the authority of a person who exercises a degree of independence from the normal chain of command."
Mr Mueller, who will have wide-ranging powers, said simply: "I accept this responsibility and will discharge it to the best of my ability."
The stakes just rose: analysis by Anthony Zurcher, BBC News, Washington
In announcing the appointment of a special counsel, Mr Rosenstein cited the "unusual circumstances" of the ongoing FBI Russia investigation. That's an understatement.
The circumstances are not just unusual, they are unprecedented. The nation has never had an administration so embattled so early in its term. There have never been such grave allegations of electoral meddling by a foreign power in a US presidential election.
Then again there has never been a president quite like Donald Trump.
Now the Russia story enters a new, more serious phase. Robert Mueller has a sterling reputation in Washington, DC. He worked with Mr Comey when the latter served as deputy attorney general in George W Bush's administration. He understands pressure-cooker politics and knows how to navigate the corridors of power.
He has wide latitude to conduct his investigation and bring criminal charges, if necessary.
While Mr Mueller is technically still part of the justice department and ultimately reports to Mr Trump, his stature is such that he is unlikely to be cowed by the president.
Independent investigations often take on a life of their own and can reach unexpected conclusions. With Mr Mueller in the game, the stakes just went up.