The president's legal team asked to stay the case while the Justice Department appeals an October decision denying its attempt to substitute as the defendant in place of President Trump.
"Mr. Trump sure seems desperate," Carroll's attorney, Joshua Matz said. "That desperation is a sign of weakness."
Carroll sued the president for defamation after he accused her of playing politics and lying about an alleged 1990s rape in a dressing room at Bergdorf Goodman.
U.S. District Judge Lewis Kaplan rejected the Justice Department's bid to replace Trump as the defendant, ruling that his statements about Carroll were not made as part of his official duties.
Matz said there should be no stay of the proceedings because the president has already "used every stall tactic in the books."
The president's attorney, Paul Burgo, said he is entitled to a stay of proceedings pending appeal but the judge appeared skeptical.
"Immunity from liability and immunity from discovery are two different things, aren't they," Kaplan asked.
"With each step forward in my lawsuit against Donald Trump, Trump's lawyers try to drag the case three steps back. More than a month ago, a federal judge told the DOJ that they couldn't take over Trump's defense, and Trump was soon going to have to turn over documents and give his DNA. Late yesterday, Trump tried to put this case on hold once again. I won't be silenced, and I look forward to having my lawyers respond to Trump's latest attempt to deny me my day in court," Carroll said in a statement.
He gave Carroll's lawyers until Dec. 17 to respond to Trump's motion.