In Beijing, where five new cases were reported on Saturday, part of the Yosemite housing complex in the northeastern district of Shunyi was locked down after an infection was found there. Residents were ordered to undergo testing.
The government said the infected person was a close contact of an earlier case in the capital.
"Please do not leave Beijing unless necessary," a spokesman for the capital's Communist Party committee, Xu Hejian, was cited as saying by state TV.
The government reported 588 new confirmed cases and no death in the 24 hours through to midnight on Friday. Its numbers are low compared with some countries, but authorities say they are ready to lock down communities if one case is found.
The Shanghai city government, where 22 new cases were reported on Saturday, announced schools would switch back to teaching online.
Public attractions including the Oriental Pearl TV tower began requiring visitors to show negative results from virus tests, according to news reports.
Hong Kong leader Carrie Lam warned the territory's wave of infections may not have peaked despite stringent controls on travel and business. It reported over 27,600 new confirmed cases.
"At this moment, we could not comfortably say that we have passed the peak," Lam said at a news conference.Â
"We'd rather take a very cautious stance."
The new cases in mainland China included 134 in Jilin province in the northeast, where the industrial city of Changchun with a population of nine million was put on lockdown Friday.
Changchun and the Jilin provincial capital, also called Jilin, are "still at the peak of community transmission," the province's party secretary, JIng Junhai, said in a statement.
On Saturday, the government announced Mayor Wang Lu of Jilin was replaced but gave no reason. The mayor of Jiutai district in Changchun also was dismissed, the Communist Party-owned Global Times newspaper reported.
Yucheng in Shandong province also was on lockdown under China's "zero tolerance" strategy, which aims to find and isolate every case.
