The city's public hospitals have been severely stretched, struggling to cope with an influx of patients including the elderly, many of whom have resisted vaccinations.
Health official Sara Ho said on Sunday that she understood public frustration but urged patients to fully cooperate with hospital staff. Health chief Sophia Chan said the government was considering tightening social distancing rules further.
While the city has so far ruled out a city-wide lockdown, authorities are examining mandatory testing for its 7.4 million people.
Sunday's COVID-19 tally was slightly higher than Saturday's 6063 cases, and the city reported 14 deaths.
The city has recorded around 40,000 infections and fewer than 300 coronavirus deaths, far below other major cities. But some epidemiologists expect daily infections to approach 30,000 by the end of March.
China has sent epidemiologists, critical care experts and over 100 testing personnel to the city, as well as mobile testing vehicles, with authorities saying the outbreak could take up to three months to stabilise.
The conversion of public housing estates, rental of commercial hotels and indoor sport centres will add an extra 20,000 extra units for people who tested positive for COVID-19 but had no or mild symptoms for isolation.
An election to choose the city's next leader, initially scheduled for March, has been postponed to May, adding to uncertainty about the former British colony's future as Beijing imposes its rule.