Leaders Re-examine U.S. Reopenings as Coronavirus Cases Hit Another Record

“This is a very dangerous time,” Gov. Mike DeWine of Ohio said in an interview on Friday, as cases were trending steadily upward in his state after appearing to be under control for more than a month. “I think what is happening in Texas and Florida and several other states should be a warning to everyone.”

“We have to be very careful,” he said.

The stock market responded badly, with the S&P 500 dropping 2.4 percent. Losses accelerated after the Texas announcement, adding to investors’ concerns that the virus continued to be a threat to the economy.

The shifting assessments of the nation’s handling of the virus stretched to the highest levels of the federal government, where Dr. Anthony S. Fauci, the director of the National Institute of Allergy and Infectious Diseases, made clear that the standard approach to controlling infectious diseases — testing sick people, isolating them and tracing their contacts — was not working. The failure, he said, was in part because some infected Americans are asymptomatic and unknowingly spreading the virus but also because some people exposed to the virus are reluctant to self-quarantine or have no place to do so.

In a brief interview on Friday, he said officials were having “intense discussions” about a possible shift to “pool testing,” in which samples from many people are tested at once in an effort to quickly find and isolate the infected.

Dr. Fauci also issued an urgent warning that while coronavirus infections were spiking mostly in the South, those outbreaks could spread to other regions.