The requests by the office of Manhattan District Attorney Alvin Bragg noted Trump's "longstanding history of attacking witnesses, investigators, prosecutors, judges and others involved in legal proceedings against him."
Trump, seeking to regain the presidency in the November 5 US election, is scheduled to go on trial in state court in Manhattan starting on March 25, one of four criminal cases against him. He has pleaded not guilty.
He is accused of falsifying business records to cover up the hush money paid to Stormy Daniels shortly before the 2016 election to keep her silent about a sexual encounter she said she had with him a decade earlier. He has denied any such relationship.
Steven Cheung, a spokesperson for Trump's campaign, said a gag order in the case would infringe on Trump's right to free speech, if implemented.
"This is election interference pure and simple," Cheung said in a statement.
Judges may impose gag orders - which restrict defendants or others involved in court cases from speaking publicly about certain aspects of legal proceedings - to try to prevent intimidation of witnesses or jurors, or to protect court staff from threats.
If approved in this case by Justice Juan Merchan, the gag order would bar Trump from "making or directing others to make" statements about witnesses concerning their role in the case.
The district attorney's office also asked that Trump be barred from commenting on prosecutors on the case - other than Bragg himself - as well as court staff members. Trump previously has called Bragg, who is a Democrat, an "animal" and a "degenerate psychopath."
Trump has argued that the case should be dismissed because it was brought for partisan purposes and because state laws do not apply to federal elections. Merchan on February 15 denied Trump's request to dismiss the charges on those grounds.
Trump has won the first five nominating contests for the Republican nomination to challenge Democratic President Joe Biden in the general election.
The measures Bragg requested are similar to restrictions a federal judge in Washington imposed last year in Trump's criminal case on charges involving his efforts to overturn the results of the 2020 election, which he lost to Biden.
In a civil fraud case, a New York state judge fined Trump a total of $US15,000 ($A22,943) for twice violating a gag order barring him from publicly talking about court staff. Trump is appealing a $US454 million judgment against him in that case.
Trump has asked an intermediate-level state appellate court to overturn Justice Arthur Engoron's February 16 ruling that he pay in penalties and interest in a civil fraud lawsuit brought in 2022 by New York Attorney General Letitia James.
The penalties, along with sizeable jury awards in two other civil cases, could become a drain on Trump's cash reserves and hobble parts of his real estate empire as he pursues the Republican nomination to challenge President Joe Biden in the November 5 US election.
James, a Democrat, accused Trump in the lawsuit of overstating his net worth by as much as $US3.6 billion in financial statements provided to banks.
Trump has accused James and Engoron of political bias against him.
