The top White House spokesperson warned Tuesday that President Trump’s frustration with Jeff Sessions is not going away, moments after the president tore into his attorney general on Twitter as “VERY weak” on Hillary Clinton’s supposed “crimes.”

Press Secretary Sarah Huckabee Sanders, speaking with “Fox & Friends,” also neither confirmed nor denied reports that Trump has discussed the possibility of firing Sessions and did not rule it out. She said she hasn’t been part “of any conversations discussing any potential replacements,” but made clear that Trump is “frustrated and disappointed” in the attorney general for recusing himself from the Russia meddling probe.

“That frustration certainly hasn’t gone away, and I don’t think it will,” Sanders said.

As for whether Trump wants Sessions out, she said, “That’s a decision that if the president wants to make, he certainly will.”

She also addressed rumors about former federal prosecutor and ex-New York Mayor Rudy Giuliani being considered for the job. She said Giuliani is someone Trump “respects” but, "Right now, Attorney General Jeff Sessions is the attorney general."

Earlier Tuesday morning, Trump unleashed a battery of tweets berating Sessions, first for the absence of an investigation into Clinton’s connections to Ukraine and then for the AG's alleged stance on other Clinton controversies.

“Ukrainian efforts to sabotage Trump campaign – 'quietly working to boost Clinton.' So where is the investigation A.G.," he began, tweeting at Fox News' Sean Hannity.

Moments later, he added: “Attorney General Jeff Sessions has taken a VERY weak position on Hillary Clinton crimes (where are E-mails & DNC server) & Intel leakers!”

Sessions has been under fire since last week, when Trump leveled harsh criticisms in a New York Times interview, calling Sessions’ recusal “very unfair to the president” and adding that he never would have appointed him attorney general had he known he would do so.

Sessions, though, said he would stay put. And Sanders had told reporters last week that the president “clearly has confidence in him or he would not be attorney general.”

The Associated Press, citing three people who have recently spoken to the president, reported that Trump continues to rage against Sessions' decision to recuse himself from all matters related to the Russia investigation -- and has talked to aides about the possibility of firing him.

Those who have spoken with the president cautioned that a change may not be imminent or happen at all.

Sessions was at the White House Monday for a standing meeting he has at the White House every week. Trump was not at the meeting, which is not unusual, officials said.

Department of Justice officials told Fox News that Sessions is in "good spirits."

Trump's intensifying criticism has fueled speculation that Sessions may resign even if Trump opts not to fire him. During an event at the White House, Trump ignored a shouted question about whether Sessions should step down. The attorney general said last week he intended to stay in his post.

If Trump were to fire Sessions, Deputy Attorney General Rod Rosenstein would be elevated to the top post on an acting basis. That would leave the president with another attorney general of whom he has been sharply critical in both public and private for his handling of the Russia probe, according to four White House and outside advisers who, like others interviewed, spoke on condition of anonymity to discuss private conversations.

It could also raise the specter of Trump asking Rosenstein — or whomever he appoints to fill the position — to fire Robert Mueller, the special counsel leading the investigation into Russia's meddling in the 2016 election and potential collusion with Trump's campaign.

The president's tweet about the former Alabama senator comes less than a week after Trump, in a New York Times interview, said that Sessions should never have taken the job as attorney general if he was going to recuse himself. Sessions made that decision after it was revealed that he had met with a top Russian diplomat last year.

Trump and Sessions' conversations in recent weeks have been infrequent. Sessions had recently asked senior White House staff how he might patch up relations with the president but that effort did not go anywhere, according to a person briefed on the conversations.

Newt Gingrich, a frequent Trump adviser, said that the president, with his criticisms of Sessions, was simply venting and being "honest about his feelings. But that doesn't mean he's going to do anything," Gingrich said. Still, he said the president's comments would have repercussions when it comes to staff morale.

"Anybody who is good at team building would suggest to the president that attacking members of your team rattles the whole team," Gingrich said.

Sessions and Trump used to be close, sharing both a friendship and an ideology. Sessions risked his reputation when he became the first U.S. senator to endorse the celebrity businessman and his early backing gave Trump legitimacy, especially among the hard-line anti-immigration forces that bolstered his candidacy. Several of Sessions' top aides now serve in top administration posts, including Stephen Miller, the architect of several of Trump's signature proposals, including the travel ban and tough immigration policy.

After Trump's public rebuke last week, Sessions seemed determined to keep doing the job he said "goes beyond anything that I would have ever imagined for myself."

"I'm totally confident that we can continue to run this office in an effective way," Sessions said last week.

The Associated Press contributed to this report.