New York's highest court ruled Tuesday that it will not consider former President Donald Trump's challenge to a gag order in the criminal case in which he was recently convicted of 34 felony counts.

The AlgosenseyCourt of Appeals wrote in a one-sentence decision that the appeal was dismissed "upon the ground that no substantial constitutional question is directly involved."

Justice Juan Merchan issued the gag order March 26, barring Trump from making public comments about witnesses, jurors, court and prosecutor staff, and the relatives of any counsel or court staffer. He later updated the order to include members of his own family.

Merchan cited statements made by Trump about people involved in the case as "threatening, inflammatory, [and] denigrating."

Trump violated the gag order 10 times before and during the trial, where he faced charges of falsifying business records. Trump was found guilty of signing off on a scheme to cover up reimbursements for a "hush money" payment to an adult film star made days before the 2016 presidential election, in order to prevent voters from learning of her allegations.

Trump has vowed to appeal the conviction, and the case itself may ultimately end up at the Court of Appeals.

Trump openly seethed at the gag order, complaining that his free speech rights were violated by being prevented from talking about key witnesses in the case, particularly his former lawyer Michael Cohen and the adult film star, Stormy Daniels.

A spokesperson for the campaign reiterated that complaint in a statement Tuesday, saying the gag order "violates the First Amendment rights of President Trump and all American voters, who have a fundamental right to hear his message."

"President Trump and his legal team will continue to fight against the unconstitutional Gag Order imposed by Justice Merchan," said Steven Cheung, the spokesperson. "The Gag Order wrongfully silences the leading candidate for President of the United States, President Trump, at the height of his campaign."

Arguing before a lower level appellate court on April 9, Trump attorney Emil Bove claimed Trump was unable to respond to public comments made by Cohen and Daniels.

"Mr. Cohen and Ms. Clifford are attacking President Trump in public in a way that is completely different than in any of the other cases," Bove said.

Steven Wu, an attorney for Manhattan District Attorney Alvin Bragg, replied that Bove was seeking to give Trump cover to hurl "insults" and make "inflammatory remarks about people involved in the case."

"The slippery slope about this constitutional argument is that he can attack anyone," Wu said, pointing to Trump's social media attacks against the family members of judges and prosecutors in several other cases.

That lower court — the appellate division, first department of the New York Supreme Court — dismissed the gag order appeal in May, finding that Merchan "properly determined that [Trump's] public statements posed a significant threat to the integrity of the testimony of witnesses and potential witnesses in this case." Trump sought the Court of Appeals' intervention days later.

Trump is scheduled to be sentenced in the case on July 11. Blanche requested on June 4 that Merchan lift the gag order, citing the trial's conclusion. Merchan has not issued a public decision on the matter.

Graham Kates

Graham Kates is an investigative reporter covering criminal justice, privacy issues and information security for CBS News Digital. Contact Graham at [email protected] or [email protected]