She added: "Is General Kelly running this country, or is the President running this country?"
Trump fired back at Manigault Newman with a tweet in which he attacked his former aide as "vicious, but not smart" and claimed that "people in the White House hated her."
"Wacky Omarosa, who got fired 3 times on the Apprentice, now got fired for the last time," Trump said. "She never made it, never will. She begged me for a job, tears in her eyes, I said Ok."
Trump said he would "rarely see" Manigault Newman in the White House, a claim that contradicts reports that she enjoyed a close relationship with the President.
In two follow-up tweets, Trump continued to disparage his former aide, saying he had "heard really bad things" about her and claiming that she "would constantly miss meetings & work."
"When Gen. Kelly came on board he told me she was a loser & nothing but problems. I told him to try working it out, if possible, because she only said GREAT things about me - until she got fired!" Trump said.
He added that while it was "not presidential" to attack her, he was doing so because he believes the media will be trying to make her "look as legitimate as possible."
The Washington Post had previously reported on Manigault Newman's account of the conversation with Trump the day after her firing. On the recording aired today, Trump is heard expressing surprise that Manigault Newman was fired.
"Omarosa, what's going on?" Trump asks. "I just saw on the news that you're thinking about leaving. What happened?"
Manigault Newman responds that Kelly told her that she had been dismissed.
"No. Nobody even told me about it," Trump replies. "You know they run a big operation, but I didn't know it. I didn't know that. Goddamnit. I don't love you leaving at all."
In an appearance on Fox News, White House spokesman Hogan Gidley declined to say whether Trump had specifically ordered Manigault Newman's firing but blasted her claims that Kelly was in charge as "absolutely ludicrous and ridiculous."
"The President makes the decisions in this White House," Gidley said. "I'm not going to get into the tick tock of who knew what and when."
Trump tweeted later that Manigault Newman "already has a fully signed Non-Disclosure Agreement!" It was not immediately clear what the President meant.
The Washington Post reported that after being fired, Manigault Newman declined a US$15,000-a-month job offer with Trump's re-election campaign, which came with a "companion agreement" including nondisclosure and nondisparagement provisions. Copies of both documents were obtained by the Post.
The "consulting agreement" describes Manigault Newman's proposed services as "speaking appearances," "fundraising appearances" and "diversity outreach."
The release of the audio comes one day after Manigault Newman shared a separate recording of what she says is the conversation in which Kelly informed her she was being fired.
In an appearance on NBC's Meet the Press, Manigault Newman said she made the recording in the Situation Room - a revelation that White House press secretary Sarah Huckabee Sanders said that, if true, "shows a blatant disregard for our national security."
Asked during today's interview about how she made the recording, Manigault Newman declined to answer, saying only, "I'll just leave that to your imagination."
She defended making recordings of her calls and meetings with Trump, Kelly and others, saying that if she hadn't, the White House would have claimed that the conversations never occurred.
"Had I not recorded this, people would say, 'She has a credibility issue,' " she said.
She also maintained that she has heard a three-minute audio recording on which Trump uses the n-word multiple times as host of The Apprentice. Manigault Newman has written that such a recording exists but has not provided evidence.
"He was talking about some African-Americans in the production during the course of The Apprentice, which is unacceptable," Manigault Newman said, urging reporters to ask Trump whether he has ever used the racial epithet.
And she took issue with the way in which the meeting to discuss her departure from the White House was handled, telling NBC, "It's not acceptable for four men to take a woman into a room, lock the door, and tell her that she cannot leave."
"The moment I said I would like to leave and they said I can't go, it became false imprisonment," she said.
Gidley disputed Manigault Newman's account of the meeting, although he declined to go into detail.
"More will come out about this, but the way she characterises that meeting is completely false," Gidley said. "Apparently telling the truth wasn't paying her bills, so she decided to switch her story just to make a quick buck."
Manigault Newman also said that she believes Trump is mentally unfit to serve as president, arguing that if Trump was telling the truth in his phone call to her the day after her firing, then he is not aware of what's going on in his own White House.
"No. I don't think he's fit," she said.
