NEW YORK — A judge held a hearing Tuesday on prosecutors' request to hold Donald Trump in contempt of court and fine him for social media posts that they say violated a gag order.

Prosecutors in the historic hush money case cited 10 posts on Trump’s social media account and campaign website that they said breached the order, which bars him from making public statements about witnesses in the case. They called the posts a “deliberate flouting” of the court’s order and said they were seeking a $1,000 fine for each one.

“The defendant has violated this order repeatedly, and he has not stopped,” said prosecutor Christopher Conroy, who said the violations continued even Monday with comments to reporters outside the courtroom about Michael Cohen, his former lawyer and fixer and the government’s star witness.

A defense lawyer responded by saying that Trump was simply responding to others' comments in the course of protected speech.

“There is no dispute that President Trump is facing a barrage of political attacks,” said attorney Todd Blanche.

The hearing could determine a potential punishment for Trump and reinforce parameters on how far the presumptive Republican nominee can go in lambasting a case that he insists constitutes political persecution. Courts in multiple cities have grappled with how to balance Trump’s political speech as a candidate with the need to protect the integrity of witnesses.

The hearing preceded the scheduled resumption of testimony in the case, with a longtime publisher expected back on the stand Tuesday to tell jurors about his efforts to help Trump stifle unflattering stories during the 2016 campaign.

David Pecker, the former National Enquirer publisher who prosecutors say worked with Trump and Cohen on a strategy called “catch and kill” to suppress negative stories, testified briefly Monday.

Pecker’s testimony followed opening statements in which prosecutors alleged that Trump had sought to illegally influence the 2016 race by preventing damaging stories about his personal life from becoming public, including by approving hush money payments to a porn actor who alleged an extramarital sexual encounter with Trump a decade earlier. Trump has denied that.

“It was election fraud, pure and simple,” prosecutor Matthew Colangelo said Monday.

Blanche countered by assailing the government's case and attacking Cohen’s integrity.

“President Trump is innocent. President Trump did not commit any crimes. The Manhattan district attorney’s office should never have brought this case,” he said.

The opening statements offered the 12-person jury and the voting public radically divergent roadmaps for a case that will unfold against the backdrop of a closely contested White House race in which Trump is not only the presumptive Republican nominee but also a criminal defendant facing the prospect of a felony conviction and prison.

The case is the first criminal trial of a former American president and the first of four prosecutions of Trump to reach a jury. Befitting that history, prosecutors sought from the outset to elevate the gravity of the case, which they said was chiefly about election interference as reflected by the hush money payments to a porn actor who said she had a sexual encounter with Trump.

“The defendant, Donald Trump, orchestrated a criminal scheme to corrupt the 2016 presidential election. Then he covered up that criminal conspiracy by lying in his New York business records over and over and over again,” Colangelo said.

Trump faces 34 felony counts of falsifying business records — a charge punishable by up to four years in prison — though it’s not clear if the judge would seek to put him behind bars. A conviction would not preclude Trump from becoming president again, but because it is a state case, he would not be able to pardon himself if found guilty. He has repeatedly denied any wrongdoing.

The case brought by Manhattan District Attorney Alvin Bragg revisits a years-old chapter from Trump’s biography when his celebrity past collided with his political ambitions and, prosecutors say, he scrambled to stifle stories that he feared could torpedo his campaign.

The opening statements served as an introduction to the colorful cast of characters that feature prominently in that tawdry saga, including Stormy Daniels, the porn actor who says she received the hush money; Cohen, the lawyer who prosecutors say paid her; and Pecker, who prosecutors say agreed to function as the campaign’s “eyes and ears.”

In his opening statement, Colangelo outlined a comprehensive effort by Trump and allies to prevent three stories — two from women alleging prior sexual encounters — from surfacing during the 2016 presidential campaign. That undertaking was especially urgent following the emergence late in the race of a 2005 “Access Hollywood” recording in which Trump could be heard boasting about grabbing women sexually without their permission.

“The impact of that tape on the campaign was immediate and explosive,” Colangelo said.

Within days of the “Access Hollywood” tape becoming public, Colangelo told jurors that The National Enquirer alerted Cohen that Daniels was agitating to go public with her claims of a sexual encounter with Trump in 2006.

“At Trump’s direction, Cohen negotiated a deal to buy Ms. Daniels’ story to prevent American voters from hearing that story before Election Day,” Colangelo told jurors.

But, the prosecutor noted, “Neither Trump nor the Trump Organization could just write a check to Cohen with a memo line that said ‘reimbursement for porn star payoff.'” So, he added, “they agreed to cook the books and make it look like the payment was actually income, payment for services rendered.”

Those alleged falsified records form the backbone of the 34-count indictment against Trump. Trump has denied having a sexual encounter with Daniels.

Blanche, the defense lawyer, sought to preemptively undermine the credibility of Cohen, who pleaded guilty to federal charges related to his role in the hush money scheme, as someone who cannot be trusted. He said Trump had done nothing illegal when his company recorded the checks to Cohen as legal expenses and said it was not against the law for a candidate to try to influence an election.

Blanche challenged the notion that Trump agreed to the Daniels payout to safeguard his campaign, characterizing the transaction instead as an attempt to squelch a “sinister” effort to embarrass Trump and his loved ones.

“President Trump fought back, like he always does, and like he’s entitled to do, to protect his family, his reputation and his brand, and that is not a crime,” Blanche told jurors.

The efforts to suppress the stories are what’s known in the tabloid industry as “catch-and-kill” — catching a potentially damaging story by buying the rights to it and then killing it through agreements that prevent the paid person from telling the story to anyone else.

Besides the payment to Daniels, Colangelo also described arrangements to pay a former Playboy model $150,000 to suppress claims of a nearly yearlong affair with the married Trump. Colangelo said Trump “desperately did not want this information about Karen McDougal to become public because he was worried about its effect on the election.”