Justice Hal Greenwald of the state Supreme Court in Poughkeepsie, New York, on Monday denied the request to stop publication and cancelled the temporary restraining order he issued on June 30 against Mary Trump and her publisher, Simon & Schuster , at the request of Robert Trump, the brother of the president.

Simon & Schuster was due to release the book on Tuesday.

Robert Trump said previously that the release of Too Much and Never Enough: How My Family Created the World's Most Dangerous Man would violate a confidentiality agreement tied to the estate of his father, Fred Trump Sr, who died in 1999. Mary Trump, a trained psychologist, is Fred Trump's granddaughter.

"Notwithstanding that the book has been published and distributed in great quantities, to enjoin Mary L Trump at this juncture would be incorrect and serve no purpose," Greenwald said in his decision.

Mary Trump's lawyer, Theodore Boutrous, said: "The court got it right in rejecting the Trump family's effort to squelch Mary Trump's core political speech on important issues of public concern."

The book's publication comes as the Republican president seeks a second term in the November 3 election. White House press secretary Kayleigh McEnany has described it as a "book of falsehoods".

Mary Trump applies her training in psychology to conclude in the book that the president likely suffers from narcissism and other clinical disorders - and was boosted to success by a father who fuelled those traits.

She writes of a "malignantly dysfunctional family" dominated by patriarch Fred Trump, who showed little interest in his five children other than grooming an heir for his real estate business.

Ultimately, he settled on Donald, she wrote, deciding his second son's "arrogance and bullying" would come in handy.

Australian Associated Press