Two days after former President Donald J. Trump was held in contempt and fined for violating the gag order placed on him in his criminal trial in Manhattan, the judge overseeing the case conducted a hearing to determine if Mr. Trump had broken the rules again.Justice Juan M. Merchan did not reach a decision on the question during the 40-minute proceeding that took place on Thursday in Manhattan Criminal Court, where Mr. Trump is being tried on charges of falsifying business records to cover up a hush-money payment to a porn star on the eve of the 2016 election.But during the hearing — the second in the past two weeks concerning violations of the gag order — Justice Merchan heard arguments from prosecutors and Mr. Trump’s lawyers about whether the former president should be sanctioned again for ignoring the protective measure four more times. The allegations stem from Mr. Trump’s recent remarks in interviews and news conferences, including one that took place outside the same courtroom where his trial is being held.On Tuesday, Justice Merchan fined Mr. Trump $9,000 for nine earlier violations. In that ruling, the judge bemoaned the fact that he lacked the authority to issue steeper fines and warned the former president that continued disobedience could land him in jail.The two contempt hearings were the latest reminder of the extraordinary measures that judges have taken to keep Mr. Trump from lashing out at participants in the wide array of legal matters in which he is embroiled.Christopher Conroy, a prosecutor, opened Thursday’s hearing by asking Justice Merchan to fine Mr. Trump $1,000 for each of the four new violations of the gag order that he said took place in recent days as the jury heard evidence.Mr. Conroy reminded the judge that he had imposed the gag order to begin with “because of the defendant’s persistent and escalating rhetoric,” adding that Mr. Trump’s “statements are corrosive to this proceeding and the fair administration of justice.”Mr. Conroy went on to say that Mr. Trump had violated the gag order not only repeatedly, but also willfully.“The defendant thinks the rules should be different for him,” he said.Todd Blanche, a lawyer for Mr. Trump, reprised arguments he made last week. He sought to persuade Justice Merchan that his client’s statements had been made merely in response to political attacks from others — including President Biden.Referring to the rows of reporters behind him in the courtroom, Mr. Blanche said that in a case that has attracted such immense publicity, it was unfair that Mr. Trump was constrained from reacting to verbal assaults.While Justice Merchan seemed open to the idea that Mr. Trump should not be defenseless against attacks from enemies or rivals, he pointed out that the gag order did not bar him from saying whatever he wished about Mr. Biden.The judge also noted that no one has forced Mr. Trump to speak daily to reporters who gather in a courtroom hallway at every break in the proceeding.“The former president of the United States is on trial, and he’s the leading candidate of the Republican Party,” Justice Merchan said. “It’s not surprising we have press in the courtroom.”The first incident the judge was asked to consider took place on April 22 as testimony began. Mr. Trump went after one of the state’s main witnesses, Michael D. Cohen, describing him as a liar to reporters outside the courtroom. Mr. Cohen, who was once a lawyer and fixer for Mr. Trump, is expected to take the stand in the coming weeks and describe how he paid $130,000 to the porn star, Stormy Daniels, on his boss’s behalf to keep her from going public with her story of a sexual encounter with him.Later that same day, Mr. Trump made disparaging remarks about jurors during a telephone interview with a right-wing media outlet, Real America’s Voice. The jury, he said, was “mostly all Democrat,” adding, “It’s a very unfair situation.”The next morning — just before he was scheduled to appear in court for a hearing on his previous violations of the gag order — Mr. Trump attacked Mr. Cohen again during a television interview with an ABC affiliate in Pennsylvania.“Michael Cohen is a convicted liar,” Mr. Trump said, “and he’s got no credibility whatsoever.”Another incident took place on April 25 when Mr. Trump, appearing at a news conference in midtown Manhattan, made a comment to reporters about David Pecker, the former publisher of The National Enquirer. Later that morning, Mr. Pecker would continue his testimony about deals he had reached with the former president to “catch and kill” negative stories about him.“He’s been very nice,” Mr. Trump said. “I mean, he’s been — David’s been very nice. A nice guy.” More