After months of denying Mueller's removal is under consideration, the change in tone came as Trump reacted furiously to an FBI raid of his private lawyer's offices on Monday.
Special counsel Mueller was appointed in May to investigate Russian efforts to tip the 2016 presidential election in Trump's favour.
US special counsel Robert Mueller. Source: AAP
Over the last year, he has increasingly dug into evidence of alleged money laundering, fraud and obstruction of justice inside Trump's inner circle.
Four Trump aides - including his 2016 campaign chair Paul Manafort and former national security advisor Michael Flynn - have already been indicted or pleaded guilty.
Now, Trump's longtime lawyer Michael Cohen - who holds secrets about many of the president's personal and financial dealings - is in the crosshairs.
"We have been advised that the president certainly has the power to make that decision," White House spokeswoman Sarah Sanders said of the possibility to remove Mueller.
"I think that the president has been clear that he thinks that this has gone too far."
Trump hunkered down at the White House, cancelling a first trip to Latin America that was due to start Friday and stewing on a move that could throw America into a constitutional crisis.
At the same time, Trump faced a momentous decision about whether to carry out military strikes in Syria.
'TOTAL WITCH HUNT'
Trump has pledged to decide by the end of Tuesday how to respond to a suspected chemical weapons attack in the rebel-held suburbs of Damascus, blamed on the Syrian regime and its allies.
But while much of his national security team debated whether strikes would be effective in deterring future chemical attacks, and how to limit the risk of escalation, Trump met his lawyers Jay Sekulow and Ty Cobb to discuss the Cohen raid.
His anger showed no signs of abating.
Michael Cohen, President Donald Trump's personal attorney. Source: AAP
"A TOTAL WITCH HUNT!!!" the president blasted on Twitter amid news that FBI agents had seized documents pertaining to his dealings with Cohen. "Attorney–client privilege is dead!"
In a phone call with CNN, Cohen admitted the raid was "upsetting to say the least."
Asked if he was worried, Cohen said: "I would be lying to you if I told that I am not. Do I need this in my life? No. Do I want to be involved in this? No."
On Capitol Hill, Republican and Democratic lawmakers urged Trump to allow Mueller to do his work.
Democrats wanted to go one step further and pass legislation protecting the Republican former FBI director.
"If the president is thinking of using this raid to fire Special Counsel Mueller or otherwise interfere with the chain of command in the Russia probe, we Democrats have one simple message for him: don't," top Senate Democrat Chuck Schumer said.
"The investigation is critical to the health of our democracy, and must be allowed to continue."
Trump's fellow Republicans said that would not be necessary, with Senate Judiciary Committee Chairman Chuck Grassley stating it would be "suicide" for the president to fire Mueller.
The raid on Cohen's offices came amid allegations he paid porn star Stormy Daniels $130,000 shortly before the election to keep a tryst with Trump quiet.
After months of silence, Trump last week offered a flat "no" when asked if he knew about the payment.
Trump's decision to scrap his trip to Colombia and Peru surprised even some White House staff.
"The president will remain in the United States to oversee the American response to Syria and to monitor developments around the world," Sanders said.
Trump had already cut the visit short - from five days, to three and, finally, to none.
The combative US president had been expected in Peru for the Summit of the Americas, where he was likely to face protests and awkward meetings with leaders who have bristled at his repeated portrayal of Latino immigrants as rapists and thugs.
Vice President Mike Pence will represent the United States in Lima instead, his aide Jarrod Agen said, adding that he would also meet Venezuelan dissidents.
Trump is still expected to travel to his Mar-a-Lago holiday home in Florida on Monday, where a summit with Japanese Prime Minister Shinzo Abe will go ahead.