WASHINGTON—Special counsel Jack Smith asked a federal appeals court on Saturday to reject Donald Trump’s claim that he is immune from prosecution on charges he plotted to overturn the 2020 election, arguing that his defense “threatens to license Presidents to commit crimes to remain in office.”

In an 82-page court filing, the special counsel’s team used some of its most strident language to date in a bid to bolster the first-ever federal prosecution of a former president. Declaring flatly that Trump is wrong, prosecutors said separation-of-powers principles, legal precedent and history combined to “make clear that a former President may be prosecuted for criminal acts he committed while in office—including, most critically here, illegal acts to remain in power despite losing an election.”