For the most part, top officials — from governors and mayors to Mr. Trump and his team — have chosen not to use masks, at least in public or at televised events, even as they encourage people to wear them. Some political analysts say image-conscious politicians may resist masks, even if they are warranted, for fear that the coverings might make them look pessimistic or nervous.

But leaders inevitably risk looking hypocritical by preaching a message about masks and then forgoing, especially when they are surrounded by aides and others. Health experts say modeling behavior is the right thing for public officials to do.

“If you’re instructing people to do stuff and you yourself aren’t doing it, that often sends the wrong message, and that’s an inconsistency in the guidance,” said Dr. Amesh Adalja, an infectious disease physician and senior scholar at the Johns Hopkins Center for Health Security.