Deputy Attorney General Rod Rosenstein, whose job hangs in the balance, will meet with President Donald Trump on Thursday, White House press secretary Sarah Sanders said Monday.

"We'll be determining what's going on," Trump said Monday afternoon before a meeting with South Korean President Moon Jae-in in New York. "We want to have transparency, we want to have openness. I look forward to meeting with him." The president also said he had talked with Rosenstein earlier Monday.

Rosenstein had been expected to learn his fate during a visit to the White House on Monday, but, with Trump in New York for a meeting of the United Nations General Assembly, any decision on his future was postponed. Rosenstein attended a regularly scheduled meeting at the White House and was still deputy attorney general when he left at midday.

The deputy attorney general spoke on Saturday with White House Counsel Don McGahn and the subject of Rosenstein's departure came up, NBC News' Pete Williams reported, though it was unclear who raised it first. Rosenstein made clear he would not accept being terminated by John Kelly, the chief of staff, according to one personal familiar with the conversation, and said it needed to come from the president himself.

However, multiple sources told NBC News that over the weekend, Trump made the decision, in conversations with staff and outside allies, not to fire Rosenstein. Among those advising Trump on this matter were the Fox News host Sean Hannity and Rep. Mark Meadows, R-N.C. Meadows wants Rosenstein to testify under oath about whether he ever contemplated wearing a wire in the presence of Trump or discussed a plan to win support from other Cabinet members to invoke the 25th Amendment to remove the president.

A person close to the White House described the current situation among the president's allies as "chaos." A second person close to the president said that if Rosenstein leaves, under any circumstances, "then the burden's on President Trump to make sure that Mueller is allowed to finish his job without interference."

Sources close to Rosenstein say he spoke to friends and former colleagues over the weekend as he raised the possibility of resigning in the wake of The Times story. One person said Rosenstein felt personally betrayed by the sources for the story, calling it a "knife in the back." Another person said Rosenstein continued to defend himself by calling the allegation that he suggested using the 25th Amendment against the president "absurd."

Rosenstein's hold on his job was imperiled after reports surfaced last week that he had discussed wearing a wire to record Trump and the possibility of organizing a push to remove the president through a process outlined in the 25th Amendment to the Constitution.

"At the request of Deputy Attorney General Rod Rosenstein, he and President Trump had an extended conversation to discuss the recent news stories," Sanders said in a statement. "They will meet on Thursday when the president returns to Washington, D.C."

Thursday is also the day Supreme Court nominee Brett Kavanaugh and Christine Blasey Ford, who has accused him of sexually assaulting her when they were in high school, are scheduled to testify before the Senate Judiciary Committee. Kavanaugh has denied her allegation.

Rosenstein's departure would throw into doubt the future of special counsel Robert Mueller's Russia probe — including whether Mueller's eventual report is ultimately delivered to Congress and made public. Trump has long been frustrated with Rosenstein over that investigation and the Justice Department's lack of action in investigating agency officials who the president believes conspired against him.

Jay Sekulow, one of Trump's personal lawyers, said on his radio show Monday that Rosenstein's ouster would demand a re-examination of the special counsel's probe.

"I think it's really important that there be a step back taken here, and a review, and I think it's a review that has to be thorough and complete, and a review that has to include an investigation of what has transpired," Sekulow said, terming such a reassessment "a timeout on this inquiry."

A new deputy attorney general should "look at all of these allegations that are both surrounding this inquiry, and that initiated this inquiry, including the Christopher Steele dossier, and the appointment of the special counsel, and how all that plays in," he said.

But it was the discussion of a wire and the 25th Amendment, first reported by The New York Times, that formed the proximate cause for Trump to justify forcing Rosenstein out.

Rosenstein said Friday that there is "no basis" for finding the president unfit to serve and that he never pursued any effort to record Trump.

Two administration officials told NBC News Friday that Rosenstein had talked about a wire sarcastically, but people who have discussed the matter with then-Acting FBI Director Andrew McCabe, who was in the meeting in question with Rosenstein, say he recalls the deputy attorney general being serious about surreptitiously taping conversations with Trump.

In an interview with Geraldo Rivera taped over the weekend, Trump said he was considering removing Rosenstein.

"Certainly it's being looked at in terms of what took place, if anything took place," Trump said. "I’ll make a determination sometime later but I don’t have the facts."

Democrats were quick to argue that Congress should intervene to shield Mueller from interference by the president.

"Congress must take immediate steps to uphold the Constitution and the rule of law — which protects all of us — by shielding the Mueller investigation against President Trump’s obstruction," Rep. Val Demings, D-Fla., said in a statement released before the announcement of the Thursday meeting between Trump and Rosenstein.

McCabe, who was fired by Attorney General Jeff Sessions, made a similar appeal.

"There is nothing more important to the integrity of law enforcement and the rule of law than protecting the investigation of Special Counsel Mueller," he said in a statement. "I sacrificed personally and professionally to help put the investigation on a proper course and subsequently made every effort to protect it. ... If the rumors of Deputy AG's Rosenstein’s departure are true, I am deeply concerned that it puts that investigation at risk.”

Secretary of State Mike Pompeo said he had "no comment" when asked about Rosenstein on Monday. Mueller's office also declined to comment on reports that Rosenstein might soon be out.