The Twitter attacks came as Vice President Mike Pence hired a personal lawyer to represent him in the intensifying investigation.
The morning missive appeared to refer to Rod Rosenstein, the deputy attorney general.
President Donald Trump could be weighing the termination of special counsel Robert Mueller from his oversight of the federal Russian Federation investigation, Christopher Ruddy, CEO of the conservative Newsmax Media and a friend of President Trump, told PBS NewsHour's Judy Woodruff on Monday. "I don't think he's really pondering it", Rep. Adam Kinzinger said.
President Trump is known to value the element of surprise.
On "Outnumbered", the former Speaker of the House said that the violent feelings of people who disagree with conservatives have been building since election night.
Despite criticism on social media from users who highlighted Gingrich's praise for Mueller upon his initial appointment last month - he had then called the appointment "superb" - Gingrich doubled down on his earlier criticisms in a phone interview with The Hill.
Mr Rosenstein has also acknowledged that "theoretically" Mr Mueller could be removed from the position as special counsel, potentially undermining his investigation.
Those kinds of arguments get no traction with prominent Trump partisans, including commentator Ann Coulter, who on Sunday evening called for Attorney General Jeff SessionsJeff SessionsSessions steps into Russian Federation crossfire Trump allies' attacks against special counsel could backfire The Memo: Trump allies turn fire on Mueller MORE to fire Mueller.
On Trump's plane ride home after a trip to Wisconsin, Sarah Huckabee Sanders told reporters he "has no intention" of firing Mueller, even though she maintained that "the president has the right to".
Trump to End 'Abusive' Individual People-to-People Travel to Cuba
President Barack Obama pursued, and secured, a thaw in relations with its longtime nemesis Cuba and the Castro government. What followed over the next two years was the most significant change in US-Cuban relations since the 1959 revolution.
Rosenstein said "I think the answer is no" but said it would depend on the circumstances.
Gingrich is correct that there is a certain partisan tilt to the team of top-notch investigators being assembled by the ex-FBI director: Jeannie Rhee, Michael Dreeben, Andrew Weissmann and James Quarles are renowned in their fields and have made repeated donations to Democrats.
They say Mr Trump did not collude with Russian Federation and see the investigation as a politically-motivated sham that handicaps his ability to execute his agenda, according to one person who advises the White House on how to handle the probe. The person spoke on condition of anonymity to discuss private conversations.
Sources have told CNN that multiple advisers have counseled Trump against firing Mueller.
If Mueller knew he was going to be named special counsel, it is unlikely he divulged that information to Trump. Brian Schatz about the scope of Sessions' recusal, Rosenstein said Sessions "actually does not know what we're investigating, and I'm not going to be talking about it publicly". "I can't imagine that anyone in the White House is seriously discussing that".
But by Sunday, Trump's lawyer Jay Sekulow refused to promise that the president would not fire Mueller.
The White House has directed questions for details to outside legal counsel, which has not responded.
Ruddy claimed that Mueller was "under consideration" to lead the Federal Bureau of Investigation, a position vacated after Trump fired James Comey, and that he spoke to the president about it.