Washington (CNN) President Donald Trump has publicly rebuked Attorney General Jeff Sessions , expressing regret for appointing him to the post and disparaging him as "beleaguered" and "very weak."

But inside the West Wing, Trump has often found himself the odd man out.

It's there that several top White House officials have urged Trump to cut out his public criticism of Sessions, making a series of arguments in Sessions' defense aimed at quelling the President's frustrations with his attorney general, two sources close to the matter told CNN.

White House chief strategist Steve Bannon, chief of staff Reince Priebus and other senior officials have talked up Sessions in conversations with Trump in recent days, reminding him that the attorney general has been one of the most effective members of his Cabinet in advocating for and advancing his agenda.

The officials have also sought to remind Trump of Sessions' longstanding political loyalty and talked up the outpouring of support Sessions received Tuesday from GOP senators, aiming to soothe Trump's angst about his pick for attorney general.

The sources, who insisted on anonymity to divulge private conversations, said Sessions supporters inside the West Wing are reminding Trump "every day, every hour" of the work Sessions has done to advance Trump's hardline on illegal immigration and tough on crime policies, both issues Trump talked up during the 2016 campaign and that are dear to his political base.

Amid those entreaties, Trump pressed his criticism of Sessions on Tuesday, but declined to say whether he wished Sessions would resign or whether he would force him out of the administration.

"I am disappointed in the attorney general. He should not have recused himself," Trump said in response to reporters' questions. "If he was going to recuse himself he should have told me prior to taking office and I would have quite simply picked something else."

Pressed on whether he wanted Sessions to go, Trump simply added: "We will see what happens. Time will tell, time will tell."

But while people close to Sessions and Trump are trying to broker a truce, one source close to the matter said mediation and lobbying efforts won't be enough to resolve the issue.

"I think it's going to take the two of them. I don't think any amount of individuals whispering in either guy's ear is going to solve it. I think the two of them have got to get together and talk it out," the source said.

Still, as of now, there is no meeting on the books for Trump and Sessions to sit down face-to-face and smooth things over, the source said.

Trump is showing no signs of backing off even as he remains surrounded by Sessions loyalists.

Beyond Bannon, who once described Sessions as a mentor, a coterie of top White House aides emerged from Sessions' world. Stephen Miller, the President's senior policy adviser and chief speechwriter, previously served as Sessions' communications director while White House deputy chief of staff Rick Dearborn was Sessions' longtime chief of staff.

But Trump's refashioned communications department is making no effort to downplay Trump's frustrations.

Sarah Huckabee Sanders, who on Friday was elevated to the press secretary role, said Tuesday morning she doesn't believe Trump's frustration with Sessions will dissipate, while newly minted communications director Anthony Scaramucci conceded that Trump "probably" does want to see Sessions exit the administration.

The talk of pushing Sessions out of the administration has rankled Republicans across Washington, from the White House to Capitol Hill, where leading Republican lawmakers rallied around the embattled attorney general, expressing confidence in his efforts and support for his decision to recuse himself from the Russia investigation.

And Breitbart News, a pro-Trump media outlet that is rarely out of lockstep with the President, on Tuesday sided with Sessions, blaring this headline on their homepage: "Trump vs. Trump: POTUS endangers immigration agenda because Sessions followed his lead on Hillary crimes."

Former House Speaker Newt Gingrich, a Trump ally who is close to several top White House officials, said Trump "ought to quit attacking (Sessions) publicly."

But he added he believes Trump's criticism was prompted by a sense that he is "drifting toward a real war."

Gingrich likened Trump's moves to publicly rebuke Sessions to his decision to bring on Scaramucci and surround himself with other brash loyalists "who are prepared to fight."

"He is clearing the decks and saying, 'These people want to destroy me,'" said Gingrich, who recently published a book titled "Understanding Trump." "That's where the recusal thing really gets to Trump."

Gingrich remained skeptical that aides' efforts to reason Trump away from his anger at Sessions will be effective.

"They'll have an impact, but Trump is a very independent person," Gingrich said. "And nobody has a decisive impact on Trump."

Even Sessions loyalists remain nervous about the attorney general's fate and are unsure that their efforts to change the President's mind will work.

And several aides have questioned in recent days whether Trump will make a major decision on Sessions without any warning -- those concerns coming days after Trump settled on Scaramucci for communications director before Bannon and Priebus had a chance to raise their objections.

"He's upset by this Russia stuff," a source close to the Trump-Sessions feud said. "What does that lead to? I don't know."