Trump has come under fire previously for using derogatory terms to refer to women and African-Americans.
At a debate during the Republican presidential primary season, he was famously asked by moderator Megyn Kelly about his tendency to call women he doesn't like "fat pigs, dogs, slobs, and disgusting animals."
More recently, Trump has repeatedly referred to Rep. Maxine Waters, D-Calif., as "low IQ" and called CNN anchor Don Lemon "the dumbest man on television."
In her book, "Unhinged," Manigault Newman claims the Trump campaign was aware of the existence of the tape from the "Apprentice" period. She describes a phone conversation about how to handle potential fallout with Lynne Patton, then an assistant to Eric Trump, a son of the president; then-Trump spokeswoman Katrina Pierson; and campaign communications director Jason Miller.
The recording played on CBS on Tuesday morning purportedly includes the voices of Patton and Pierson. CBS said it had not confirmed the authenticity of the tape.
On the tape, a person whom Manigault Newman identifies as Pierson is heard saying: "I'm trying to find out at least the context it was used in to help us figure out a way to spin it."
A person Manigault Newman says is Patton then describes having a conversation with Trump about the alleged tape: "I said, 'Well, sir, can you think of anytime this might have happened?' and he said, 'No.'"
"Well, that's not true," Manigault Newman then says on the tape.
The person said to be Pierson later says: "No, he said it. He is embarrassed."
In a joint statement after Manigault Newman's appearance on CBS, Pierson and Patton said that "no one ever denied the existence of conversations about a reported 'Apprentice' tape" and that they occurred because "Omarosa was obsessed with it."
In her book, Manigault Newman says she understands that Trump used the slur "multiple times throughout the show's taping during off-camera outtakes, particularly during the first season of the Apprentice."
In tweets Monday, Trump attacked his former aide as "vicious, but not smart" and claimed that "people in the White House hated her."
His latest attack on Manigault Newman prompted immediate criticism from lawmakers and others.
"The president of the United States is calling a woman of color 'a dog.' How dare he!" Rep. Frederica S. Wilson, D-Fla., said during an interview on CNN. "He has taken this country to its knees."
House Minority Leader Nancy Pelosi, D-Calif., responded to Trump's tweet with one of her own directed toward the president, which said: "#BeBest."
That is the name of the initiative recently launched by first lady Melania Trump that calls for children to speak online with "respect."
Sen. Jeff Flake, R-Ariz., called the language used by Trump "unbecoming of a President of the United States."
"There is no excuse for it, and Republicans should not be okay with it," Flake, a frequent Trump critic, said in a tweet.
Even some Trump friends suggested that the president had gone too far on Tuesday.
During an appearance Tuesday morning on Fox News, White House counselor Kellyanne Conway did not directly answer a question about whether Trump's use of the term "dog" was appropriate.
Conway said she was disappointed with Manigault Newman, whom she had considered "a colleague and a friend."
"The best play for Omarosa would have been to take credit for a lot of the great things that Donald Trump has done for this country, including for African Americans," Conway said.
Conway said that she has never heard Trump use a racial slur and that Manigault Newman never relayed concerns to her about hearing one.
"She never pulled me aside, never said to me, 'Hey, listen, I heard the president say this and I don't know what to do with it.'"
On Twitter, Trump has compared other people to dogs in the past but rarely called them dogs.
Trump, for instance, said that Mitt Romney "choked like a dog" when he ran for president. Trump said David Gregory was "fired like a dog" from his job as moderator of "Meet the Press" on NBC. And he said Sen. Ted Cruz, R-Texas, "lies like a dog" when he courts the support of evangelical voters.
Trump takes legal action against Omarosa
US President Donald Trump's campaign has filed an arbitration action against Omarosa Manigault Newman, alleging that the former White House aide, who just published a tell-all book, has broken a 2016 confidentiality agreement.
The action, which the campaign said was filed in New York, comes amid a publicity tour by Manigault Newman to promote her book, Unhinged, which portrays Trump as bigoted and racist and questions his mental capacity.
The Washington Post has not seen a nondisclosure agreement signed by Manigault Newman during the campaign, but copies of other agreements signed by aides include broad prohibitions on behaviour and appear to be drawn heavily from similar contracts used by the Trump Organisation, the President's family firm.
Under one such agreement, signers promised not to "demean or disparage publicly" Trump, his company or any member of his family. Signers also agree to participate in binding arbitration at Trump's discretion if a dispute arises over the agreement. Trump also reserves the right to take signers to court.
Trump has threatened legal action against book authors and other perceived adversaries in the past but has not followed through on many occasions.
It was not immediately clear what Trump's campaign, which was headquartered in New York in 2016, was hoping to achieve with its action filed with the American Arbitration Association.
A lawyer for Manigault Newman declined immediate comment.
The action comes as Trump has sought to publicly disparage Manigault Newman, the former reality television star who was the highest-ranking black employee in the White House.
After requiring nondisclosure agreements of campaign aides, Trump has sought NDAs from dozens of White House aides, according to current and former administration employees.
In her book, Manigault Newman writes that the Trump campaign offered her a US$15,000-a-month job upon leaving the White House in exchange for signing a broadly worded NDA that would have barred her from disclosing details of her tenure in the administration. That agreement was never signed, she says.
Trump pointed out on Twitter yesterday that Manigault Newman had signed an earlier agreement.