Arizona’s Republican governor shut down bars, movie theatres, gyms and water parks on Monday amid an alarming resurgence of coronavirus cases nationwide.
Meanwhile leaders in several states ordered residents to wear masks in public in a dramatic course reversal.
Mr Trump has refused to wear a mask during visits to states and businesses that require them.
Arizona Governor Doug Ducey’s order went into effect immediately and will last for at least 30 days.
Mr Ducey also ordered public schools to delay the start of classes until at least August 17.
Arizona health officials reported 3,858 more confirmed coronavirus cases on Sunday, the most reported in a single day in the state so far and the seventh time in the past 10 days that daily cases surpassed the 3,000 mark.
Since the pandemic began, 74,500 cases and 1,588 deaths stemming from the virus have been reported in Arizona.
“Our expectation is that our numbers next week will be worse,” Mr Ducey said Monday.
The state is not alone in its reversal. Places such as Texas, Florida and California are backtracking, closing beaches and bars in some cases amid a resurgence of the virus.
In New Jersey, Governor Phil Murphy announced on Monday that he is postponing the restarting of indoor dining because people have not been wearing face masks or complying with recommendations for social distancing.
Democratic governors in Oregon and Kansas said on Monday that they would require people to wear masks.
Idaho is moving in a different direction, at least when it comes to the elections.
Despite the continuing spread of the virus, state elections officials have said that they would allow in-person voting — as well as mail-in ballots — for August primaries and the November general election, the Idaho Statesman reported.
Idaho’s May 19 primary was the first statewide election held by mail only. The primary had record voter turnout.
In Texas, a group of bar owners sued on Monday to try to overturn Republican Governor Greg Abbott’s order closing their businesses.
They contend Mr Abbott does not have the authority, and they complained that other businesses, such as nail salons and tattoo studios, remain open.
“Governor Abbott continues to act like a king,” said Jared Woodfill, attorney for the bar owners.
“Mr Abbott is unilaterally destroying our economy and trampling on our constitutional rights.”
“States that were recalcitrant … are doing a 180, and you have the same states now wearing masks,” Mr Cuomo said.
“Let the president have the same sense to do that as an executive order, and then let the president lead by example and let the president put a mask on it, because we know it works.”
Less than a week after Jacksonville Mayor Lenny Curry said there would be no mask requirement, city officials announced on Monday that coverings must be worn in “situations where individuals cannot socially distance”.
White House spokeswoman Kayleigh McEnany responded by saying the president’s advice is to “do whatever your local jurisdiction requests of you”.