The White House says it will decide "soon" on the fate of Attorney General Jeff Sessions, after a barrage of criticism from President Donald Trump.
In a Twitter onslaught, Mr Trump called the country's top prosecutor "weak", a day after labelling him "beleaguered".
At the White House later, Mr Trump said he was "disappointed" with Mr Sessions.
The former Alabama senator should not have recused himself from an FBI inquiry into alleged Russian meddling in the election, said the president.
Allies of Mr Sessions have indicated that he intends to stay in his post.
"Attorney General Jeff Sessions has taken a VERY weak position on Hillary Clinton crimes (where are E-mails & DNC server) & Intel leakers!" Mr Trump tweeted on Tuesday.
Will Sessions get fired?
Anthony Scaramucci, the president's new communications director, fanned speculation on Tuesday that the attorney general's days could be numbered.
"We'll come to a resolution soon," he said when asked by reporters about the tensions between the Republican president and top prosecutor.
An interviewer put it to Mr Scaramucci that it was pretty clear Mr Trump wants Mr Sessions gone.
"If there's this level of tension in the relationship that's public, you're probably right," Mr Scaramucci said.
Mr Sessions was in the West Wing on Monday, but did not meet the president, according to deputy press secretary Sarah Huckabee Sanders.
The attorney general has recently asked White House aides if he can see Mr Trump to patch things up, reports AP news agency.
But Mr Scaramucci said on Tuesday: "My guess is the president doesn't want to do that."
Analysis: No one is safe
Anthony Zurcher, BBC North America reporter
Another day, another 24 hours of Jeff Sessions gently fluttering in the breeze.
Although Donald Trump denied it on Tuesday afternoon, it's hard to read his "we'll see what happens" and "time will tell" comments - when asked if he would fire Mr Sessions - as anything but ominous.
Even more concerning for the attorney general were the president's remarks to the Wall Street Journal earlier in the day, essentially shrugging off the then-senator's early endorsement of his presidential candidacy.
Mr Sessions was more than just a Trump bandwagoner. He was a Trump trailblazer. He staked out anti-immigration positions long before the New York mogul took the presidential dive. He was an animated advocate for Mr Trump on the campaign trail, sticking by him when other national politicians ran for cover.
Now the president is turning on his loyal ally.
The prospect that even Mr Sessions isn't above attack is sending a chill throughout conservative ranks. His former Senate colleagues, currently debating healthcare reform, have to wonder whether the president has their back.
Conservative media - even reliably pro-Trump Breitbart.com - are balking at the president's barbs. Within the executive branch, unease grows.
If Cabinet secretaries aren't safe from the president's sting, who is?
Why is Trump unhappy with Sessions?
Mr Sessions, known for his hardline anti-immigration stance, was one of then-candidate Mr Trump's earliest supporters in Washington.
But in March he recused himself from the Russia inquiry after failing during his confirmation hearing to disclose a meeting with the Kremlin's envoy.
What's the reaction from Congress?
The most powerful Republican on Capitol Hill, House of Representatives Speaker Paul Ryan, has made clear he would have no problem if Mr Sessions is dismissed.
Mr Ryan told reporters on Tuesday: "He [President Trump] determines who is hired and fired in the executive branch - that's his prerogative."
But Republican South Carolina Senator Lindsey Graham defended Mr Sessions.
"President Trump's tweet today suggesting Attorney General Sessions pursue prosecution of a former political rival is highly inappropriate," tweeted Mr Graham.
Some suspect Mr Trump's ultimate target is Robert Mueller, the special counsel who is leading the Russia investigation.
Representative Adam Schiff tweeted on Tuesday that Mr Trump "wants to force Sessions to resign so he can appoint someone to curb Mueller probe".
Mr Schiff is ranking Democrat on the House Intelligence Committee, one of several congressional panels investigating whether Trump election campaign officials colluded with Moscow.
What next if Sessions is axed?
It was reported on Monday that the president is considering former New York Mayor Rudy Giuliani or Texas Senator Ted Cruz for the job.
But Mr Giuliani told CNN on Monday that Mr Sessions had "made the right decision under the rules of the justice department" in recusing himself from the inquiry.
If Mr Trump were to fire Mr Sessions, Deputy Attorney General Rod Rosenstein would be next in line to take over the job on an acting basis.
However, Mr Trump has been critical of Mr Rosenstein for his handling of the Russia inquiry.
Why does Trump want Clinton investigated?
During the election, Mr Trump suggested the Democratic candidate would be in jail if he were elected.
Chants of "lock her up" were routine at his rallies as he stoked voter mistrust over Mrs Clinton's use of a private email server while she was secretary of state.
But it was Mr Trump who dropped the issue once he was elected.
In an interview with the New York Times, he said: "I don't want to hurt the Clintons, I really don't.
"She went through a lot and suffered greatly in many different ways."