NEW YORK — Manhattan prosecutors suggested Friday that Donald Trump violated a gag order in his hush-money criminal case this week by assailing the judge’s daughter and making a false claim about her on social media.

The Manhattan district attorney’s office asked Judge Juan M. Merchan to “clarify or confirm” the scope of the gag order, which he issued Tuesday, and to direct the former president and presumptive Republican nominee to “immediately desist from attacks on family members.”

In a letter to Merchan, Assistant District Attorney Joshua Steinglass argued that the gag order’s ban on statements meant to interfere with or harass the court’s staff or their families makes the judge’s daughter off-limits from Trump’s rhetoric. He said Trump should be punished for further violations.

Trump’s lawyers contended the D.A.’s office is misinterpreting the order and said it doesn’t prohibit him from commenting about Loren Merchan, a political consultant whose firm has worked on campaigns for Trump’s rival. President Joe Biden, and other Democrats.

“The Court cannot ‘direct’ President Trump to do something that the gag order does not require,” Trump’s lawyers Todd Blanche and Susan Necheles wrote to Merchan in a response to the prosecution’s letter. “To ‘clarify or confirm’ the meaning of the gag order in the way the People suggest would be to expand it.”

The trial, which involves allegations Trump falsified payment records in a scheme to cover up negative stories during his 2016 presidential campaign, is scheduled to begin April 15. Trump denies wrongdoing and has pleaded not guilty to 34 counts of falsifying business records.

In his posts Wednesday on his Truth Social platform, Trump wrote that Loren Merchan “makes money by working to ‘Get Trump,'” and he wrongly accused her of posting a social media photo showing him behind bars.

A spokesperson for New York’s state court system said Trump’s claim was false and that the social media account Trump was referencing no longer belonged to Loren Merchan.

The account on X, formerly known as Twitter, “is not linked to her email address, nor has she posted under that screenname since she deleted the account. Rather, it represents the reconstitution, last April, and manipulation of an account she long ago abandoned,” court spokesperson Al Baker said.