Justice Juan Merchan challenged a defence assertion that Trump did not violate the gag order when he said the Manhattan jury in the first criminal trial of a former US president was picked from a heavily Democratic area.
"I'm making an argument that he didn't," Trump lawyer Todd Blanche told the judge.
"Well I'm not agreeing with that argument," Merchan responded without saying whether or when he would impose a fine.
Prosecutors are asking Merchan to fine Trump $US4,000 ($A6,120) for violating the gag order four times last week.
In one instance, the Republican Trump said in a TV interview that "that jury was picked so fast - 95 per cent Democrats. The area's mostly all Democrat".
"By speaking about the jury at all, he places this proceeding in jeopardy," prosecutor Christopher Conroy said.
Conroy said Trump also violated the gag order by calling his former lawyer Michael Cohen a liar and former National Enquirer publisher David Pecker a "nice guy".
Pecker testified last week and Cohen is expected to be a crucial witness in the case.
Blanche said there was "no threat" in what Trump said about Pecker and said Cohen, in his social media comments, has been "inviting, and almost daring" Trump to respond to his comments about the trial.
Any penalty would follow a $US9000 fine Merchan imposed on Tuesday.
Merchan said at that session that he might jail Trump if he continues to defy the gag order.
Conroy said prosecutors were not yet asking for Trump to be jailed.
The gag order aims to prevent one of the world's most prominent people from intimidating witnesses, jurors and other participants in the trial.
It does not prevent Trump from criticising prosecutors or the judge himself.
On Thursday, Merchan appeared skeptical of Blanche's argument that the gag order prevents Trump from responding to political attacks while he seeks to win back the White House in a November 5 election.
Prosecutors are asking a judge to fine Donald Trump for violating a gag order with public comments. (AP PHOTO)
"Everybody else can say whatever they want about this case," Blanche said.
"They're not defendants in this case," Merchan responded.
Trump claims prosecutors are working with Democratic President Joe Biden to undercut his bid to win back the White House and says Merchan faces a conflict of interest because his daughter has done work for Democratic politicians.
"I don't think there's ever been a more conflicted judge - crooked and conflicted," Trump said at a rally in Michigan on Wednesday.
Trump is accused of falsifying business records to hide a hush-money payment to porn star Stormy Daniels shortly before the 2016 presidential election.
Trump has pleaded not guilty and says he did not have sex with Daniels, whose real name is Stephanie Clifford.
The hearing about the gag order took place at the start of the day in the absence of the 12 jurors and six alternates.
The jurors were later brought in to hear testimony from lawyer Keith Davidson, who helped arrange the payment to Daniels, who was shopping her story of a 2006 sexual encounter with Trump to media outlets at a time when Trump was already facing damaging accusations of sexual misbehaviour.
Davidson confirmed that Daniels signed a non-disclosure agreement with Trump but said he would not describe the payment as hush money.
"It was consideration in a civil settlement agreement," he said.
Davidson said the forceful denial he helped Daniels craft when the payment was revealed in 2018 did not amount to a lie because it referred to a "romantic sexual" relationship rather than a one-off sexual encounter.
"You have to go through it word by word, and I think if you did so, it would technically be true with an extremely fine reading," Davidson said.
Daniels later disavowed the statement and said the signature on it was not hers.
