WASHINGTON—A federal appeals court on Friday largely upheld a gag order imposed on Donald Trump in the criminal case alleging he conspired to overturn his 2020 election loss, but it narrowed the restrictions to allow the former president to publicly criticize special counsel Jack Smith.

In a partially sealed 68-page opinion, a three-judge panel of the U.S. Court of Appeals for the D.C. Circuit affirmed provisions of the October gag order barring Trump from attacking witnesses, other prosecutors, court staff as well as their families, but said it “sweeps in more protected free speech than is necessary” by protecting Smith himself.