WASHINGTON—A federal appeals-court panel sharply questioned prosecutors and Donald Trump’s defense lawyers alike on Monday as it weighs whether to affirm restrictions on what the former president can say about his election-interference case.

The hearing before a three-judge panel of the U.S. Court of Appeals for the District of Columbia Circuit was the latest clash between Trump’s lawyers and special counsel Jack Smith’s team over a gag order issued last month by Trump’s trial judge, Tanya Chutkan.