The governors expressed astonishment. “You want to now say the federal government is in charge?” Gov. Andrew M. Cuomo of New York said on MSNBC. “Which by the way is a shift because the federal government didn’t close down the economy, right? They left it to the states. It was state by state, it was a whole hodgepodge, the governors had to close the economy, which was not politically easy to do, but now the federal government says it can open it? Well then, why didn’t you close it if you can open it?”

Even some sympathetic constitutional scholars said Mr. Trump could not. “There is no authority for a president to order states to ‘open up’ if the state believes that such an order would be inimical to public health,” said Jonathan Turley, a law professor at George Washington University who testified last year against impeachment in the House. “The president had no authority to order a national lockdown and certainly does not have authority to now order the lifting of such orders issued by governors.”

That does not mean that Mr. Trump’s decision on reopening the country is not meaningful. Even if he does not have direct authority to impose his will, any guidelines he issues may go a long way toward setting a standard that states and cities could follow, especially in Republican states that have taken their lead from him.

But some critics said he looked like he was debating himself at the podium. “I think the thing that’s unsettling to the public isn’t just the absence of consistent guidance,” said David Axelrod, a former adviser to President Barack Obama. “It’s the revelation that the person in charge is unsure.”

With Mr. Trump’s approval ratings slipping, some of his conservative allies are concerned that he is not connecting with his core base of supporters.

Conservative organizations plan to join forces to weigh in on when and at what level certain parts of the country can be reopened. They plan to stay in touch with health professionals working within the White House and outside it, but there is some worry about waning patience with big government spending to relieve the effects of the virus, according to a person familiar with the discussions.

“The government needs to start looking at how we can quickly begin to reopen the economy in stages and communicate that plan, but it’s also vital that states and the federal government reduce the excessive regulatory burden to reignite the economy when we get back to work,” said David McIntosh, the president of the Club for Growth, a conservative advocacy group.