An inquiry into possible links between Russia and the Trump election campaign will be led by ex-FBI director Robert Mueller.
The appointment comes amid a growing Democratic outcry for someone outside the US Justice Department to handle the politically charged investigation.
It follows the claims that fired FBI chief James Comey wrote in a memo that President Donald Trump had asked him to end an investigation into former national security adviser Michael Flynn.
Earlier Mr Trump claimed that “no politician in history” has been “treated worse or more unfairly” than he has.
He was speaking on the day he faced calls to be impeached over his handling of the Comey scandal and his relationship with Russia.
Offering “advice” to new recruits at a coastguard graduation ceremony in New London, Connecticut, he quickly turned the focus on his recent difficulties.
“Over the course of your life you will find that things are not always fair,” he said.
“You will find that things happen to you that you do not deserve, and that are not always warranted, but you have to put your head down and fight, fight, fight!”
Mr Trump added: “Never, ever, ever give up – things will work out just fine.
“Look at the way I’ve been treated lately – especially by the media.
“No politician in history … has been treated worse or more unfairly.
“You can’t let them get you down. You can’t let the critics and the naysayers get in the way of your dreams.
“I guess that’s why we won.
“Adversity makes you stronger – don’t give in, don’t back down and never stop doing what you know is right.
“Nothing worth doing ever, ever, ever came easy.”
Earlier, Vladimir Putin said he was willing to hand over a transcript of a discussion between Mr Trump and senior Russian officials.
The US President allegedly disclosed highly classified informationabout “terrorism and airline flight safety” while meeting foreign minister Sergei Lavrov and ambassador Sergei Kislyak at the White House last week.
However, Mr Putin said Mr Trump did not pass over secrets and dismissed the scandal as “political schizophrenia”.