Thirty-seven states are seeing sustained reductions in cases, with only one reporting significant increases. Arizona and California, which reached disastrous new case records in recent weeks, have reported noticeable drops over the past several days. Around some Midwestern cities that drove surges of infections in the early fall, case numbers have fallen 50 percent or more from their peaks.

Still, the country continues to average nearly 190,000 new cases each day, more than any point of the pandemic before December. Deaths from the coronavirus are still extraordinarily high, with more than 4,300 deaths announced on Wednesday, the second-highest daily total of the pandemic. And in some places, there has been no progress at all.

Virginia is reporting some of its highest infection numbers yet. New outbreaks are raging in South Carolina. And in parts of Texas, including around San Antonio and along portions of the Mexican border, case numbers are as high as they have ever been. The county that includes Laredo is reporting more than 500 cases each day, a per capita figure more than twice as high as Los Angeles County, which is also struggling.

In places that have seen a slowing of new cases in recent days, local and state health officials were sharing positive — but tentative — news about the virus.

“Everything’s moving the right way,” a smiling Dr. Allison Arwady, the commissioner of public health for Chicago, said at a news conference on Thursday, noting that because of encouraging metrics in the city, museums have reopened, gyms are allowing group classes and more restrictions could be loosened in the coming days. Epidemiologists say that cases rise and fall in cycles controlled almost entirely by human behavior, and some experts worried that new openings of businesses, permitted because of sinking case numbers, might just set off new surges once more.

Gretchen Musicant, the Minneapolis commissioner of health, said that officials in the state were “encouraged, but wary” of the situation, and that they continue to be watchful as Minnesota begins reopening certain sectors of the economy once again.

“We’re watching to make sure that those reopenings don’t escalate our rates again,” Ms. Musicant said.

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