The rise of new cases came as Chinese leaders told Wuhan to set up mass quarantine centers for people with the coronavirus. The death toll and number of infections continued to soar in China, officials said.

The authorities in Wuhan declared that the city would be locked down as they tried to contain the virus’s spread. The cordon that was first imposed around the city of 11 million quickly expanded to roughly 50 million people in the province of Hubei.

Wuhan and Hubei have borne the brunt of the epidemic as the shutdown of transportation links into and around it slowed down the transportation of vital medical supplies. The fatality rate in Wuhan is 4.1 percent and 2.8 percent in Hubei, compared to just 0.17 percent elsewhere in mainland China.

The Chinese government says the quarantine has prevented a broader outbreak in the rest of the country,

“This is almost a humanitarian disaster” for the central Chinese region, said Willy Lam, an adjunct professor at the Center for China Studies at the Chinese University of Hong Kong, who cited insufficient supplies of medical equipment, food and other necessities. “The Wuhan people seem to be left high and dry by themselves.”

Health officials said that 563 people had died from the virus, up from nearly 500 people the day before, and that 28,018 cases had been confirmed. On Monday, the number of confirmed cases was put at 20,438, meaning the number increased more than 35 percent in just a few days.

Many doctors believe that the number of deaths and infections are undercounted because hospitals and laboratories are under severe strain to test for the virus. Local officials in Hubei Province have called on health care workers to speed up the process.

Many sick residents in Hubei have been turned away by overstretched hospitals, which lack test kits and beds. The widening scope of the new virus has strained China’s health care system and has sealed off more cities, canceled public gatherings and shut down schools.

A senior Chinese official has ordered a round up all residents in the city who have been infected with the coronavirus and place them in isolation, quarantine, or in designated hospitals.

Sun Chunlan, said city investigators should go to each home to check the temperatures of every resident and interview infected patients’ close contacts.

“Set up a 24-hour duty system. During these wartime conditions, there must be no deserters, or they will be nailed to the pillar of historical shame forever,” Ms. Sun said.

The city’s authorities have set up a mass quarantine shelters this week. But concerns are growing about whether the centers, which will house thousands of people in large spaces, will be able to provide even basic care to patients and protect against the risk of further infection..

When Ms. Sun inspected one of the shelters, set up in Hongshan Stadium on Tuesday, she emphasized that anyone who should be admitted must be rounded up, according to a Chinese news outlet, Modern Express. “It must be cut off from the source!” she said of the virus. “You must keep a close eye! Don’t miss it!”

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