The gag order, issued by Judge Juan Merchan in the criminal case against Trump, remains in effect.
Separately, Trump has asked Merchan to terminate the gag order ahead of his sentencing scheduled for July. The former president was convicted of 34 counts of business fraud relating to hush money payments to adult film star Stormy Daniels.
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Trump's lawyers did not immediately respond to a request for comment.
In March, just before the trial started, Merchan granted prosecutors' request for a gag order that precluded Trump from making public statements about any witnesses in the case, jurors, prosecutors, court staff, or members of their family. Trump was not restricted from commenting on the judge or Manhattan District Attorney Alvin Bragg.
Merchan fined Trump $10,000 and found him in criminal contempt for violating the gag order 10 times early in the trial and raised the prospect that he might have to jail Trump if he continued to do so.
In their filing with the appeals court, Trump's attorneys argued that the case presents "substantial constitutional questions of the highest importance."
"This Gag Order restricts President Trump's core political speech on matters of central importance at the height of his Presidential campaign, where he is the leading candidate, and thus it violates the fundamental right of every American voter to hear from the leading candidate for President on matters of enormous public importance," his attorneys wrote.
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Trump's lawyers said that the case still presents substantial constitutional questions even though the trial has ended, adding that the gag order does not include a set termination date.
If the Court of Appeals did find the gag order unconstitutional, Trump's attorneys wrote it would "undermine the justification" for the fines Trump received for his violations.
In their own filing, Bragg's office urged the court to dismiss the appeal, arguing that Trump has a "well-documented history of leveling threatening, inflammatory, and denigrating remarks against trial participants."
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