Chinese authorities extended a lockdown in Shanghai to cover all of the financial center's 26 million people on Tuesday after city-wide testing saw new COVID-19 cases surge to more than 13,000 amid growing public anger over quarantine rules.

The lockdown now covers the entire city after restrictions in its western districts were extended until further notice, in what has become a major test of China's zero-tolerance strategy to eliminate the novel coronavirus.

At least 38,000 personnel have been deployed to Shanghai from other regions in what state media has described as the biggest nationwide medical operation since the shutdown of the city of Wuhan in early 2020 after the first known coronavirus outbreak there.

Shanghai's quarantine policy has been criticised for separating children from parents and putting asymptomatic cases among those with symptoms.

A temporary treatment area had opened a 1,000-bed section for treating parents and children, the Shanghai Children Medical Center said on its social media account, but it was not clear if the new section indicated a wider change of policy.

As a growing number of members of the public shared comments and videos across social media expressing frustration with the lockdown, authorities showed no sign of wavering.

"Shanghai's epidemic prevention and control is at the most difficult and most critical stage," Wu Qianyu, an official with the municipal health commission, told a briefing.

"We must adhere to the general policy of dynamic clearance without hesitation, without wavering."

Wu did not comment on Tuesday on the uproar over children being separated from their parents but on Monday she insisted that positive children had to be kept apart.

Shanghai residents organised an online petition calling for asymptomatic children to be allowed to isolate at home, with at least 1,000 people signing but as of Tuesday, it was no longer accessible on the WeChat messaging app.

'Nobody knows'

Shanghai imposed tough restrictions last week as it struggled to contain what has become its biggest COVID-19 outbreak, after originally taking a more targeted approach.

Thousands of residents have been locked up in rudimentary quarantine facilities after testing positive, whether they are symptomatic or not.

Jane Polubotko, a Ukrainian marketing manager being held in the city's biggest quarantine centre, told Reuters it was not clear when they would be released.

"Nobody knows how many tests we need to get out," she said.

Chen Erzhen, a doctor in charge of one Shanghai quarantine facility, said in an interview with the People's Daily at the weekend that it was possible that authorities would revise guidelines and allow asymptomatic people to stay home, especially if the number of cases mounted.

"The most important thing is the problem of personal compliance," he said.

Sun Chunlan, vice-premier in charge of COVID-19 prevention, urged grassroots Communist Party organisations to "do everything possible" to help residents solve problems, such as access to medicine, food and water.

Shanghai reported a record 13,086 new asymptomatic coronavirus cases on Monday, authorities said, up from 8,581 the previous day, after more than 25 million people were swabbed in 24 hours in the city-wide testing campaign.

The government said it collected 25.7 million samples in 2.4 million test tubes, and almost 80% of the total had been tested by Tuesday morning. Positive results are followed up on an individual level.

The proportion of asymptomatic cases is far higher in Shanghai than the rest of the world, which has been attributed to a screening process that catches infected people before they become ill.

However, experts said it did not explain why symptomatic cases fell on Monday to 268, from 425 the previous day.

Meanwhile, the costs to the world's second-biggest economy mount.

Some 23 Chinese cities are under total or partial lockdown, affecting an estimated 193 million people in areas accounting for 13.6% of its gross domestic product, the Nomura brokerage said in a note on Tuesday.