U.S. President Donald Trump escalated his long-running feud with Attorney General Jeff Sessions on Friday, pressing him to investigate those who are probing his administration.

Responding to Sessions's declaration that he would not be influenced by politics, Trump tweeted that Sessions must "look into all of the corruption on the 'other side,'" adding: "Come on Jeff, you can do it, the country is waiting!"

“Department of Justice will not be improperly influenced by political considerations.” Jeff, this is GREAT, what everyone wants, so look into all of the corruption on the “other side” including deleted Emails, Comey lies & leaks, Mueller conflicts, McCabe, Strzok, Page, Ohr...... —@realDonaldTrump

....FISA abuse, Christopher Steele & his phony and corrupt Dossier, the Clinton Foundation, illegal surveillance of Trump Campaign, Russian collusion by Dems - and so much more. Open up the papers & documents without redaction? Come on Jeff, you can do it, the country is waiting! —@realDonaldTrump

The president's tweets marked the second day of a highly public smackdown by Trump of his attorney general.

Earlier this week, Trump, concerned by the legal downfall of two former advisers, accused Sessions of failing to take control of the Justice Department. Sessions punched back Thursday, saying he and his department "will not be improperly influenced by political considerations."

Trump's anger with Sessions boiled over in an interview Thursday on Fox News in which the president also expressed frustration with the plea agreement his onetime legal "fixer" Michael Cohen cut with prosecutors, including implicating Trump in a crime that Cohen admitted.

But the U.S. president also feels that flipping 'almost ought to be illegal' 0:40

Trump said it might be better if "flipping" — co-operating with prosecutors in exchange for more favourable treatment — were illegal because people co-operating with the government "just make up lies" to get favourable treatment.

Trump on Friday also addressed the five-year sentence given to a former government contractor convicted of mailing a classified U.S. report to a news organization.

Ex-NSA contractor to spend 63 months in jail over “classified” information. Gee, this is “small potatoes” compared to what Hillary Clinton did! So unfair Jeff, Double Standard. —@realDonaldTrump

Earlier, he defended himself on Fox against talk of impeachment — "the market would crash ... everybody would be very poor" — tried to dissociate himself from Cohen, and said anew that he hadn't known in advance about Cohen's hush money payments to silence women alleging sexual relationships with the celebrity businessman.

Trump's latest shots against law enforcement came as he appeared increasingly vulnerable to long-running investigations after this week's one-two punch of Cohen's plea deal and the conviction of Trump's former campaign chair Paul Manafort.

Trump has spent more than a year publicly and privately venting over Sessions's decision to recuse himself from the federal Russia-collusion investigation because he had worked on Trump's campaign. Trump, who blames that decision for the eventual appointment of special counsel Robert Mueller, told Fox and Friends host Ainsley Earhardt that Sessions "never took control of the Justice Department and it's a sort of an incredible thing."

'Unprecedented success'

"What kind of man is this?" Trump asked.

"You know the only reason I gave him the job? Because I felt loyalty, he was an original supporter," Trump said of Sessions, an Alabama Republican who was the first senator to endorse Trump's bid.

Sessions has made it clear to associates that he has no intention of leaving his job voluntarily despite Trump's constant criticism. But his tone in his statement on Thursday made clear he is tired of the president's attacks.

Sessions, shown at a news conference on Wednesday in Cleveland, has said the Justice Department will not be 'improperly influenced by political considerations.' (Tony Dejak/Associated Press)

"I took control of the Department of Justice the day I was sworn in, which is why we have had unprecedented success at effectuating the president's agenda."

He said that while he's attorney general, the department "will not be improperly influenced by political considerations. I demand the highest standards, and where they are not met, I take action."

Allies, including Republican members of Congress, have long advised Trump that firing Sessions — especially before the midterm elections — would deeply damage the party.

But South Carolina Sen. Lindsey Graham, who in March said firing Sessions would "blow up" the judiciary committee, has been shifting his tone.

"I think there will come a time, sooner rather than later, where it will be time to have a new face and a fresh voice at the Department of Justice," he told reporters on Thursday. "Clearly, Attorney General Jeff Sessions doesn't have the confidence of the president."