Governors wrestle with how to reopen and face new challenges to their authority.

The sweeping orders that kept roughly nine out of 10 Americans at home in recent weeks gave way on Friday to a patchwork of state and local measures that would allow millions of people to return to restaurants, movie theaters and malls for the first time in a month or more.

But as more states, like Texas, prepared to reopen on Friday, the governors of California and Michigan were contending with challenges to their authority to shutter at least some parts of public life.

In Lansing, Mich., hundreds of protesters — many of them armed — gathered at the State Capitol on Thursday to oppose stay-at-home orders, weeks after a larger gathering on April 15, when thousands of demonstrators mobilized by conservative groups created a traffic jam on the streets around the statehouse.

And in California, Gov. Gavin Newsom stepped in on Thursday to shut down the beaches in Orange County, rolling back earlier attempts at giving people there a chance to stroll along the shore while staying a safe distance away from one another.

Now Mr. Newsom, already the target of litigation for his stay-at-home order, is facing fresh resistance: The Huntington Beach City Council voted Thursday night to sue the state over the beach ban, and the City Council in nearby Newport Beach appeared poised to follow, according to local media reports.

The protest in Michigan came as Gov. Gretchen Whitmer, a Democrat, signed three orders extending the restrictions to combat the virus. State Senator Dayna Polehanki shared a photograph of protesters with rifles inside the building, as well as a video of hundreds of people outside. It is legal to carry firearms inside the State Capitol.

President Trump on Friday urged Ms. Whitmer to “give a little,” writing that the protesters were “very good people, but they are angry.”