New York prosecutors say they are open to a partial lifting of a judge's gag order now that Republican presidential candidate Donald Trump has been convicted on criminal charges stemming from an effort to influence the 2016 election by buying a porn star's silence.

Prosecutors in Manhattan District Attorney Alvin Bragg's office said in a court filing dated Thursday and made public on Friday that they supported allowing him to speak publicly about witnesses in the case.

But they urged Justice Juan Merchan to keep in place restrictions on his comments about jurors, court staff and individual prosecutors, citing risks to their safety.

In the first criminal trial of a U.S. president, a Manhattan jury on May 30 found Trump guilty of covering up his former lawyer Michael Cohen's $130,000 hush money payment to adult film actress Stormy Daniels, who was threatening to go public before the election with her story of a sexual encounter with Trump.

Trump, elected to a four-year term in 2016, denies the alleged 2006 encounter and has vowed to appeal his conviction. Sentencing is scheduled for July 11, four days before his party convenes to formally nominate him for president ahead of the Nov. 5 election.

Trump's lawyers did not immediately respond to a request for comment on Friday.

They had asked to lift the gag order, arguing it was stifling his ability to respond to attacks by political opponents. They complained he was barred from responding to public attacks from Cohen and Daniels, who testified on behalf of the prosecution at trial.

They said it was particularly important ahead of Trump's debate next Thursday with his rival, Democratic President Joe Biden, who has called Trump a convicted felon.

It was unclear when Merchan would rule on any modifications to the gag order. The judge fined Trump $10,000 for violations of the order during the seven-week trial and warned him on May 6 that he would be jailed if he ran afoul of the order again.

Merchan imposed the gag order before the trial began in April, finding that Trump's history of threatening statements posed a risk of derailing the proceedings.

Prosecutors said the gag order does not prohibit Trump from criticizing the verdict, the case in general, Bragg or Merchan.

"Many of the defendant's complaints simply ignore the narrowness of this Court's orders," they wrote in the filing.

The prosecutors said the restriction on Trump's comments about trial witnesses no longer needed to be enforced.

But they said: "Defendant's supporters, following his lead, have attempted to identify jurors and threatened violence against them."

"There thus remains a critical need to protect the jurors in this case from attacks by defendant and those he inspires to action," they wrote.

Defense lawyers previously argued that holding Trump accountable for "harassing communications" by "independent third parties" violated his right to free speech.