"On the other hand the non-confidential part of the Agreement, the Trump family relationships may be more interesting now in 2020 with a Presidential election on the horizon," the judge said.
He also wrote that Robert Trump had not shown any damages that the book's publication would cause himself or the public.
Robert Trump is not frequently mentioned in the book that seeks to trace how family members were affected by the President's father, a successful real estate owner, and how the President may have developed some of the traits that have been most apparent at the White House.
Mary Trump, a trained psychologist and Donald Trump's only niece, wrote in the book that she had "no problem calling Donald a narcissist — he meets all nine criteria as outlined in the Diagnostic and Statistical Manual of Mental Disorders."
The judge reversed orders he had issued temporarily blocking Mary Trump and her publisher, Simon & Schuster, from publishing or distributing a tell-all book about the President. An appeals judge had already lifted the order blocking Simon & Schuster.
The book, Too Much and Never Enough: How My Family Created the World's Most Dangerous Man, was originally to be published at the end of July.
The publisher announced last week it would be published tomorrow. Mary Trump's lawyer, Theodore Boutrous, said the judge "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 First Amendment forbids prior restraints because they are intolerable infringements on the right to participate in democracy. Tomorrow, the American public will be able to read Mary's important words for themselves," he said.
In a statement, Simon & Schuster said it was "delighted that the Court has denied the plaintiff's request for preliminary injunction, and vacated the Temporary Restraining Order against our author, Mary L. Trump."
It added: "The unfettered right to publish is a sacred American freedom and a founding principle of our republic, and we applaud the Court for affirming well-established precedents against prior restraint and pre-publication injunctions," it added.
"'TOO MUCH AND NEVER ENOUGH' is a work of great significance, with very real implications for our national discourse, and we look forward to bringing it to a public that is clearly eager to read it."
Messages seeking comment were left with a lawyer for Robert Trump.
On the eve of its publication, Mary Trump's book was ranked No. 1 on the Amazon.com list of best-selling books.
-AP
