"President Trump's political opponents have, and will continue to, attack him based on this case," his lawyers wrote. "The voters have the right to listen to President Trump's unfettered responses."
They said the order sought by Manhattan District Attorney Alvin Bragg's office would prevent Trump, the Republican frontrunner to challenge Democratic President Joe Biden, from speaking on a campaign issue in the run-up to the Nov. 5 U.S. presidential election.
Gag orders restricting defendants from speaking publicly about certain aspects of legal proceedings may be imposed to try to prevent intimidation of witnesses or jurors, or to protect court staff from threats.
Bragg's office last year charged Trump with 34 counts of falsifying business records to cover up his lawyer Michael Cohen's $130,000 payment to Daniels shortly before the 2016 election to keep her silent about a sexual encounter she said she had with Trump a decade earlier.
Trump has pleaded not guilty and denied any such relationship.
Prosecutors last month asked New York Supreme Court Justice Juan Merchan, who is trying the case, to bar Trump from making public comments about witnesses or court staff ahead of the trial, the first-ever of a former U.S. president.
The prosecutors cited what they called Trump's "longstanding history of attacking witnesses, investigators, prosecutors, judges and others involved in legal proceedings against him."
Trump's lawyers wrote he should be able to respond to public attacks by potential witnesses such as Cohen and Daniels, whose real name is Stephanie Clifford.
The measures Bragg requested are similar to restrictions a federal judge imposed last year in a criminal case on charges involving Trump's efforts to overturn his loss to Biden in the 2020 election. Trump has pleaded not guilty in that case.
In a civil fraud case, a New York state judge fined Trump a total of $15,000 for twice violating a gag order barring him from publicly talking about court staff. In that case, Trump is appealing a $454.2 million penalty for misstating the values of his family real estate company's properties to dupe lenders.
Trump's lawyers did not object to a separate request from prosecutors for the jurors' identities to be disclosed only to the lawyers in the case and Trump himself.
But his lawyers asked that Merchan allow their identities to be disclosed to consultants hired by lawyers to assist with the jury selection process.
