Simon & Schuster said in a statement, "We support Mary L. Trump's right to tell her story in 'Too Much and Never Enough, ' a work of great interest and importance to the national discourse that fully deserves to be published for the benefit of the American public".
He said Mary was violating a non-disclosure agreement she signed in 2001 after the same court settled a contentious fight over the estate of real estate tycoon Fred Trump - the father of Donald and Robert and of Mary's father Fred Trump Jr, who died in 1981.
Robert Trump, who is the President's younger brother is the one who filed the restraining order last week to block the book.
In the book, Mary, a 55-year-old clinical psychologist, recounts what she witnessed of the "toxic family" in the home of her grandparents, according to her publisher.More news: China takes aim at 4 United States media companies, demanding staff, business info
"Short of corrective action to immediately cease their egregious conduct, we will pursue this case to the very end", Mr Harder said. "We will immediately appeal", Boutrous said.
In court papers filed on Tuesday, Simon & Schuster claimed that tens of thousands of copies of the book had already been printed, adding that it is a best seller on Amazon.
Trump on Thursday said in a court filing that she would not have consented to a secrecy deal that was part of a legal settlement two decades ago over the wills of the president's parents had she known that the financial valuations underlying the agreement were false.
The issue, as the attorneys state it, is "w$3 hether the [trial judge's] Order constitutes an unconstitutional prior restraint of Simon & Schuster's rights under the First Amendment of the United States Constitution and Article I, Section 8 of the New York Constitution".
Robert Trump, in a statement through his lawyer, Charles Harder, said he was "very pleased" by the judge's ruling, according to The New York Times.More news: Samsung not to attend IFA 2020: Report #116929
The book, titled "Too Much and Never Enough: How My Family Created the World's Most Dangerous Man", has already ascended to the top of bestseller lists based on pre-sales, underscoring the intense interest in a rare insider account by a member of the Trump family. Now her book describes a "nightmare" of family dysfunction.
The president's niece claims that after she filed objections, the three siblings, including Donald Trump, cut off her health insurance coverage.
He said she has caused "enormous damages" through her "breach of contract", according to The Washington Post.
Simon & Schuster, which also published a book from former White House adviser John Bolton, said it is disappointed by the court's decision.More news: Choreographer Saroj Khan passes away at 71