WASHINGTON—Producers and distributors of medical supplies across the country are raising red flags about what they say is a lack of guidance from the federal government about where to send their products, as hospitals compete for desperately needed masks and ventilators to combat the spread of the novel coronavirus.

The issue is taking on greater urgency as supplies run short in hard-hit regions. New York City Mayor Bill de Blasio, for example, said the city could run out of supplies after a week, saying in a CNN interview...