Florida has seen its average new daily cases increase more than tenfold since it began reopening in early May. Cases in Arizona have jumped by 858 percent since beginning to reopen May 8. Cases in Texas have risen by 680 percent since beginning to reopen May 1.

Epidemiologists had warned that reopening could lead to waves of new infections if it was done before the virus was contained, and before contact tracing was sufficiently ramped up enough to contain future outbreaks.

The trajectory taken by many states that pushed to reopen early offers a cautionary tale.

South Carolina, one of the first states to let retail stores reopen, has seen its average daily case count rise to 1,570, up from 143 from when the state began to reopen in late April, a 999 percent increase. And in Georgia, where the governor’s moves to reopen swiftly in late April were criticized as too aggressive by Mr. Trump — who had generally been pushing states to move faster to reopen — cases have risen by 245 percent.

Now the U.S. is debating when and how to reopen school classrooms — which Mr. Trump is pushing for strongly, even as school districts, teachers and some parents express concerns — and which steps should be taken by states that have become hot spots, from reimposing restrictions to ordering people to wear masks.

Many of the states that bore the brunt of cases in March and April but were slower to reopen have seen significant decreases in reported cases since. Average daily cases in New York are down 52 percent since the state began to reopen in late May, and they are down 83 percent in Massachusetts.

There are exceptions, though. California, once seen as a model for how to contain the virus, has seen an alarming increase in new cases, which are up 275 percent since May 25.