Donald Trump is under fire for saying the FBI's reputation is "in tatters" over its probe into alleged collusion between Russia and his campaign.
Ex-FBI head James Comey and ex-attorney general Sally Yates, who were both fired by Mr Trump, led the criticism.
Republican Senator Lindsey Graham said his comments and tweets on ongoing investigations were at his "own peril".
Meanwhile, the US president's critics suggested he could have admitted obstructing justice in a tweet.
Mr Trump posted a barrage of criticism on Sunday morning, saying the FBI's reputation was "in tatters" and was the "worst in history", while again accusing it of failure in its treatment of his former opponent for the presidency, Hillary Clinton.
Mrs Clinton was investigated by the FBI ahead of the election after it emerged she had used a private email server to conduct state department business, but no charges were brought against her or her team.
After years of Comey, with the phony and dishonest Clinton investigation (and more), running the FBI, its reputation is in Tatters - worst in History! But fear not, we will bring it back to greatness.— Donald J. Trump (@realDonaldTrump) December 3, 2017
The president seized on news that an FBI officer had been dismissed from the investigation after he was discovered to have made anti-Trump remarks in text messages, tweeting: "Report: 'ANTI-TRUMP FBI AGENT LED CLINTON EMAIL PROBE' Now it all starts to make sense!"
Mr Trump denies that his team colluded with Russia to get him elected, but four members of his inner circle have now been charged as part of the FBI inquiry lead by Robert Mueller.
Former acting attorney general Sally Yates hit back at Mr Trump, tweeting that "the dedicated men and women of the FBI deserve better" and that the "only thing in tatters is the president's respect for the rule of law".
The former director of the FBI, James Comey, who was fired by President Trump and has testified in the investigation, posted a strong rebuttal of the president's criticism of the organisation.
He posted online a quote from himself in June that said: "I want the American people to know this truth: The FBI is honest. The FBI is strong. And the FBI is, and always will be, independent."
The Comey-Flynn controversy
Last week Mr Trump's former national security adviser Michael Flynn admitted to lying to the FBI.
On Saturday a post on Mr Trump's Twitter account appeared to suggest that he had known Mr Flynn had lied, contradicting his own account from the time.
I had to fire General Flynn because he lied to the Vice President and the FBI. He has pled guilty to those lies. It is a shame because his actions during the transition were lawful. There was nothing to hide!— Donald J. Trump (@realDonaldTrump) December 2, 2017
A White House lawyer later said he had written the tweet and that the controversial line had actually been an error.
On Monday Mr Trump said that he felt badly for Mr Flynn.
Speaking to reporters, he said: "Hillary Clinton lied many times to the FBI, nothing happened to her. Flynn lied and they destroyed his life, I think it's a shame."
The president fired Mr Flynn in February for misrepresenting the nature of his contacts with Russian ambassador Sergei Kislyak to Vice-President Mike Pence.
Then-FBI director James Comey alleges that in a private meeting the day after Mr Flynn was fired, the president asked him to show leniency to the dismissed aide, saying, "I hope you can see your way clear to letting this go, to letting Flynn go."
Tweeting on Sunday, Mr Trump issued a fresh denial that he had pushed Mr Comey to drop the investigation into Mr Flynn.
I never asked Comey to stop investigating Flynn. Just more Fake News covering another Comey lie!— Donald J. Trump (@realDonaldTrump) December 3, 2017
Senior Democrats and legal experts said that if Mr Trump had known Mr Flynn had lied, then tried to get Mr Comey not to investigate him, that could be tantamount to obstruction of justice.
The row soured what should have been a celebratory weekend for the president, after his sweeping tax reform bill scraped through the Senate early on Saturday morning.