Hong Kong's health facilities have been overloaded by an "onslaught" of COVID-19 infections, its leader said, as a rise in omicron cases threatens to bring down the city's "zero-COVID" policy.

Authorities have adhered to mainland China's policy of stamping out the smallest outbreak with mass quarantine, widespread tracking and prolonged social distancing measures since the start of the pandemic.

But the extremely contagious omicron variant breached the Chinese territory's defenses in late December, piling up more than 8,000 infections in a few weeks with researchers warning that daily cases could exceed 25,000 by next month.

While the infection rate remains low compared to major cities around the world, Hong Kong's policy of sending even asymptomatic cases to hospitals and quarantine facilities has filled up beds and amplified wait times.

"The onslaught of the fifth wave of the epidemic has dealt a heavy blow to Hong Kong and overwhelmed the city's capacity of handling," leader Carrie Lam said in a statement issued Sunday night.

The surge in cases has increased wait times "for admitting people who test positive to isolation facilities," she added.

Surrounded by patients queuing for tests all of last week, the city's hospitals on Sunday told people who have "stable or have mild symptoms" to stay at home.

But Lam said the government "will spare no effort to implement" the "zero COVID" strategy and that China will help the city to bolster testing and quarantine resources.

Hong Kong has struggled to persuade its elderly population to get vaccinated with only around 50% of people over the age of 70 receiving a jab.

The government has repeatedly said its "zero COVID" policy is to buy more time for them to get inoculated.

Researchers warned Friday that by the end of March, the city could be racking up 28,000 daily infections. By the end of 2021, Hong Kong had only recorded a touch over 12,000 cases.

Last week marked the city's first COVID-19 deaths in five months, with seven patients over 70 and one 4-year-old boy falling to the virus.