On Thursday, the U.S. set another record for new daily cases, more than 86,600, topping the record set last Friday when the country recorded 85,000. It’s the equivalent of about one new case every second.

“There is no way to sugarcoat it: We are facing an urgent crisis, and there is an imminent risk to you, your family members, your friends, your neighbors,” said Gov. Tony Evers of Wisconsin.

Over the past week, new cases in the United States have averaged more than 75,000 a day, and eight states reported daily records on Thursday. More total cases have been identified in the U.S. than in any other country, though some nations have had more cases in proportion to their populations.

In Wisconsin, more than 200 coronavirus deaths have been announced over the last week, and as case numbers explode, hospitals have been under increasing strain.

Wisconsin, home to eight of the country’s 15 metro areas with the highest rates of recent cases, was among the first states to lose control of the virus this fall. But the surge that started in the Upper Midwest and rural West has now spread far beyond, sending infection levels soaring in places as disparate as El Paso, Chicago and Rexburg, Idaho.

Idaho’s governor, Brad Little, this week imposed new restrictions on businesses and gatherings. “Hospitals throughout the state are quickly filling up or are already full with Covid-19 patients and other patients, and way too many health care workers are out sick with Covid-19,” Mr. Little said.

Twenty-one states added more cases in the seven-day period ending Wednesday than in any other seven-day stretch of the pandemic against a backdrop of a bitter presidential contest.

President Trump, in the closing days of his campaign, has assured voters that the virus is vanishing, brushing aside the devastation it has wrought and even mocking people who take precautions — including measures his own health advisers recommend — to slow the spread of the disease.

Daily reports of deaths from the virus remain far below their spring peaks, averaging around 780 a day. But those, too, have started to tick upward.

There are not many hopeful signs in the recent data.

Reports of new cases are increasing in 42 states. Northeastern states, including New Jersey and Rhode Island, are seeing infection numbers rise after months of stability. And in North Dakota, where more than 5 percent of the population has now tested positive —  the biggest share of any state — reports of new cases continue to soar.