Federal prosecutors on Sunday asked the judge handling former President Donald J. Trump’s trial on charges of plotting to overturn the 2020 election to reject his request to freeze the case in its entirety as Mr. Trump appeals her recent ruling that he is not immune from prosecution.

The prosecutors told the judge, Tanya S. Chutkan, that even as the former president’s appeal of the immunity decision moved forward, she should continue working on several of the unresolved legal issues in the case and not postpone the trial’s current start date of March 4.

“During the pendency of the appeal, any number of matters could arise in this case that are not involved in the appeal,” wrote Molly Gaston, a top deputy to Jack Smith, the special counsel who is overseeing Mr. Trump’s federal prosecutions. “The court should not enter an order preventing it from handling them.”

“For its part,” Ms. Gaston went on, “in light of the public’s strong interest in a prompt trial, the government will seek to ensure that trial proceeds as scheduled.”