But Mr. Trump’s advisers are divided about the wisdom of encouraging the protests. At some of them, Gov. Gretchen Whitmer of Michigan, a Democrat, has been compared to Adolf Hitler. At least one protester had a sign featuring a swastika.

One adviser said privately that if someone were to be injured at the protests — or if anyone contracted the coronavirus at large events where people were not wearing masks — there would be potential political risk for the president.

But two other people close to the president, who asked for anonymity in order to speak candidly, said they thought the protests could be politically helpful to Mr. Trump, while acknowledging there might be public health risks.

One of those people said that in much of the country, where the numbers of coronavirus cases and deaths are not as high as in places like New York, New Jersey, California and Washington State, anger is growing over the economic losses that have come with the stringent social-distancing restrictions.