Lawyers for former President Donald J. Trump asked a federal appeals court on Wednesday to avoid setting an expedited schedule as it considered the issue of whether Mr. Trump was immune from charges accusing him of plotting to overturn the 2020 election.

In a 16-page filing that blended legal and political arguments, the lawyers asked a three-judge panel of the court not to move too quickly in mulling the question of immunity, saying that a “reckless rush to judgment” would “irreparably undermine public confidence in the judicial system.”

“The manifest public interest lies in the court’s careful and deliberate consideration of these momentous issues with the utmost care and diligence,” wrote D. John Sauer, a lawyer who is handling the appeal for Mr. Trump.

The former president’s brief to the U.S. Court of Appeals for the District of Columbia Circuit was the first time he formally weighed in on how fast his critical appeal of the immunity issue should be heard.

The filing came two days after the special counsel, Jack Smith, asked the same judges to fast-track the appeal, saying that keeping the underlying case moving forward would vindicate the public’s interest in a speedy trial.

Mr. Smith has also filed a parallel request to the Supreme Court, asking the justices to consider the immunity issue even before the appeals court does and to issue their decision quickly. Mr. Trump’s lawyers have until Dec. 20 to respond to that request.