A top Chinese health official warned on Sunday that the spread of the dangerous new coronavirus, already extraordinarily rapid, is accelerating further, deepening global fears about an illness that has sickened more than 2,700 people worldwide and killed at least 80 people in China. The grim diagnosis came amid concerns that China’s efforts to contain the spread of the disease, despite a lockdown of unprecedented scope affecting 56 million people, may not only have come too late but could even make the situation worse, including by exacerbating shortages of medical supplies.

Adding to the growing global alarm, people who are carrying the virus but not showing symptoms may still be able to infect others, according to the Chinese official, Ma Xiaowei, the director of China’s National Health Commission. Such asymptomatic transmissions would make the disease much more difficult to control, as seemingly healthy people travel and interact with others. “The epidemic is now entering a more serious and complex period,” Mr. Ma said during a Sunday news conference in Beijing. “It looks like it will continue for some time, and the number of cases may increase.”

China’s attempts to curb the disease’s spread — essentially cordoning off the major cities in the province of Hubei, including its capital, Wuhan, a city of 11 million people — are a “public health experiment, the scale of which has not been done before,” said Dr. William Schaffner, an infectious disease expert at Vanderbilt University. “Logistically, it’s stunning, and it was done so quickly.”