The new coronavirus, though most serious in China, “holds a very grave threat for the rest of the world,” Tedros Adhanom Ghebreyesus, the director general of the World Health Organization, said at a forum in Geneva on Tuesday.

As the outbreak’s health implications have mounted, so has its political toll: It is already one of the most significant crises for the central government in decades. China’s ruling Communist Party dismissed two health officials in Hubei, the province at the center of the epidemic, and replaced them with a leader sent from Beijing. They were the first senior officials to be punished for the government’s handling of the outbreak.

This week, the Chinese authorities urged factory workers and farmers to get back to work. But at the same time, other officials warned that there may be new outbreaks in the coming weeks — particularly in three populous provinces, Zhejiang, Guangdong and Henan — as migrant workers return to their jobs after the Lunar New Year break.

They also highlighted the role of clusters, which they defined as two or more infections within a relatively small area, in accelerating the disease’s spread.

Wu Zunyou, the chief epidemiologist of China’s Center for Disease Control and Prevention, said at a news conference on Tuesday that there had been nearly 1,000 clusters in China, with 83 percent occurring within families. But schools, factories, shopping centers and medical facilities also contributed to the spread, he said.

In Tianjin, more than 600 miles from Wuhan, officials have taken drastic steps to contain a cluster of cases linked to the department store in the district of Baodi. An outbreak in that city could be especially troublesome for the central government: It is only a half-hour from Beijing by high-speed train.

At least 33 of the city’s 102 confirmed patients worked or shopped at the department store, or had close contact with employees or customers, according to local health authorities. Of those, many — including the latest patient, a 31-year-old woman announced on Tuesday — had no history of travel to Wuhan.