US President Donald Trump celebrated Friday after a major Republican Party donor cut ties with Steve Bannon, a former key adviser who contributed to a newly published book that questions the head of state's fitness for office.

Trump made the remarks on Twitter after billionaire Republican donor Rebekah Mercer said she was no longer supporting Bannon, who was a senior adviser to the real-estate tycoon during the campaign and served as the president's White House chief strategist from January-August 2017.

"The Mercer Family recently dumped the leaker known as Sloppy Steve Bannon. Smart!" Trump tweeted.

In a statement Thursday, Mercer - a major shareholder in Trump-supporting online news outlet Breitbart News, whose executive chairman is Bannon - said she supports Trump and his agenda and that she and her family "have provided no financial support to (Bannon's) political agenda, nor do we support his recent actions and statements."

Trump's feud with Bannon, who has been a prominent supporter of the president's "America First" agenda, particularly his hard-line stance on immigration and opposition to trade deals like the Trans-Pacific Partnership, stems from the former adviser's comments to Michael Wolff, author of a new book that provides a highly unflattering look at the current occupant of the White House.

In "Fire and Fury: Inside the Trump White House," released Friday, Bannon tells Wolff that a June 2016 meeting in which several of then-candidate Trump's top campaign officials sat down with a group of Russians - apparently in hopes of obtaining damaging information on Democratic nominee Hillary Clinton - was "treasonous" and "unpatriotic."

In that gathering at Trump Tower in New York, Donald Trump, Jr.; the president's son-in-law, Jared Kushner; and Trump's then-campaign chairman, Paul Manafort, met with Kremlin-linked lawyer Natalia Veselnitskaya and others.

A special prosecutor, former FBI Director Robert Mueller, is investigating that meeting as part of his wide-ranging probe into possible collusion between the Trump campaign and Russia to damage Clinton's candidacy.

One of Trump's attorneys, Charles Harder, sent a cease-and-desist letter to Bannon this week that says his remarks to Wolff violated a confidentiality agreement and warns him of imminent legal action.

Harder also sent a similar letter to Wolff demanding that he immediately cancel plans to publish his new book.

The letter says that "actual malice (reckless disregard for the truth) can be proven by the fact the Book admits in the Introduction that it contains untrue statements" and "appears to cite to (sic) no sources for many of its most damaging statements about Mr. Trump."

Wolff, who says his book is based on more than 200 interviews with the president and members of his political circle, on Friday defended the content of his tell-all in an exclusive interview on NBC's "Today" show and said he had spoken to Trump on the record.

He said "100 percent of the people" around the president question his fitness for office and see him as a "child" with a "need for immediate gratification."

Earlier, Trump had taken to Twitter to lash out at Wolff.

"I authorized Zero access to White House (actually turned him down many times) for author of phony book! I never spoke to him for book. Full of lies, misrepresentations and sources that don't exist. Look at this guy's past and watch what happens to him and Sloppy Steve!" he tweeted late Thursday.