China wants to set aside the iron-fisted “Covid-Zero” lockdown measures it has become known for in favor of a more precise approach to containing Covid-19 that is less damaging to the country’s economy.

A record surge in Covid-19 infections, fueled by the highly infectious Omicron variant, is putting that strategy to its toughest test yet, with implications for global business and China’s ability to eventually find a path out of its containment strategy.

Chinese leader Xi Jinping highlighted the urgency and difficulty of the challenge Thursday at a meeting of the Communist Party’s ruling Politburo Standing Committee, where he demanded officials rush to get infections under control, but also strive to “minimize the impact of the Covid situation on economic and social development.”

The updated measures, including more efficient testing and shorter and more targeted quarantines, appear to be producing desired results in some cities.

In Shanghai, the site of one local outbreak, Tesla Inc. and Volkswagen AG factories have been able to restart production after 48-hour suspensions, compared with the weeks it took many Chinese businesses to resume following harsh lockdowns early in the pandemic.

The southern metropolis of Shenzhen, also hit with a surge of infections, said Thursday that it would allow companies to resume work if they could meet epidemic prevention criteria after it suspended nonessential businesses in a week-long containment program it described as “slow living.”

China’s National Health Commission allowed the use of antigen-based tests, which are faster and easier to administer.

Photo: TINGSHU WANG/REUTERS

Elsewhere, officials had to fall back on older, heavier-handed methods. When infections started spreading, residents in the northeastern province of Jilin were hit with restrictions on travel and movements reminiscent of the harsh lockdown imposed on the city of Wuhan and surrounding Hebei province in early 2020, and again on the city of Xi’an this past winter.

On Friday, China’s National Health Commission said daily numbers of new locally transmitted cases rebounded to 4,130, up from 2,432 cases the previous day but still a thousand cases lower than the record number reported on Monday. The country has recorded a total of roughly 17,000 new cases since Sunday.

While those numbers are minuscule compared with other countries hit by Omicron, the surge in cases is nevertheless a problem for China’s leadership. While China’s economy weathered the first part of the pandemic better than most, an effort by Mr. Xi to remold the economy by tightening controls on private business dented growth. The war in Ukraine has put additional pressure on China, politically as well as economically, in a year in which Beijing is putting a premium on economic stability.

The new Covid-19 outbreak has further eroded confidence in the Chinese economy, despite a strong start to the year, with analysts predicting the country would struggle to hit its annual 5.5% growth target, announced earlier this month.

Health officials in different localities gathered Friday morning to discuss Mr. Xi’s comments, according to people familiar with the discussions. One main takeaway, they said, was that the current surge had reinforced the need to move away from stringent lockdowns to more precise and cost-effective measures that keep businesses and supply chains functioning.

The contrast between the old “Covid-Zero” approach and the new one, which the government refers to as “dynamic clearing,” is most visible in the country’s biggest cities.

When officials in Beijing discovered a small outbreak at a local market in the summer of 2020, authorities resorted to what they described as “wartime-like measures,” dispatching armies of neighborhood-watch volunteers to conduct mass testing and seal off entire housing compounds for weeks at a time.

When cases began spreading in Shanghai this month, local authorities instead used shorter rolling lockdowns of individual residential buildings wherever they detected a high risk of exposure, which they lifted after two days if all residents tested negative.

In Shenzhen, restrictions have varied from district to district based on risk level. While those living in high-risk areas have been asked to stay at home, others are allowed to step out.

Howe Huang, a 29-year-old internet company employee based in Shenzhen’s low-risk Nanshan district, said he is able to register for a “travel slip” from his housing compound management to go on his daily jog or walk. Restaurants are closed for dine-in services, but they still provide takeout and delivery, he said.

In an update to its pandemic-control playbook, the National Health Commission this week lowered its testing threshold for recovered patients to be released from quarantine. It also allowed the use of antigen-based tests, which are less accurate than nucleic-acid tests but faster and easier to administer.

A temporary Covid-19 testing facility in Yantai, China, this month.

Photo: str/Agence France-Presse/Getty Images

The new guidance also said asymptomatic patients and those with mild symptoms should go to centralized isolation facilities, to free up hospital resources for the treatment of more serious cases. Government data so far have shown that the overwhelming majority of new cases are mild or asymptomatic.

The difference for companies has in some cases been significant. Foxconn Technology Group, a major assembler of Apple Inc.’s iPhones, took roughly two months to resume production in its Chinese plants after the country’s first round of lockdowns in 2020. On Wednesday, the company said its campus in Shenzhen would reopen in an Olympics-style bubble environment just two days after it suspended activities.

Tesla’s factory in Shanghai resumed production early Friday after a similar two-day suspension, as workers who tested negative were allowed to return from truncated quarantines, according to people familiar with the matter.

Some regions are still resorting to older methods. For the most part, they tend to be poorer cities and provinces without the resources or tools to use nimbler methods, according to Chinese health officials and financial analysts.

That dynamic has played out in Jilin, a province of 24 million in China’s northeastern rust belt with a local gross domestic product less than a third as large as Shanghai’s. Travel in and out of the province has been restricted and all residents have been subjected to multiple rounds of mass testing. Millions of people have been ordered to stay indoors, allowed out one every other day to buy food and other necessities.

Although its production site in Shanghai is operational, Volkswagen’s plants in Changchun, capital of Jilin, remained closed as of Friday. The province continues to account for the vast majority of new cases, with 2,626 on Friday. Shanghai and Shenzhen, meanwhile, had 260 and 105 new cases, respectively.

Considering how Omicron has overwhelmed other countries, including those that had previously succeeded in containing the virus, China’s ability to keep infection numbers from exploding further has been impressive, according to Yanzhong Huang, a health expert at the Council on Foreign Relations in New York.

“It shows China’s state capacity,” said Mr. Huang.

China could bring the cases under control as early as April, he said, though even then the country would still need to prepare for and then deal with the inevitable next outbreak, which will continue to be very costly.

China has planned to keep some form of Covid-19 containment regime in place at least until next spring, after Mr. Xi secures an expected third term as Communist Party leader. Mr. Xi’s comments this week didn’t suggest a change in those plans, according to Chinese health officials.

Zhang Wenhong, one of China’s top infectious disease experts, said on Thursday during a press conference that China should use the time it was buying with its Covid-19 control measures to increase vaccination, secure the availability of antiviral drugs for treating Covid-19 and improve its healthcare capacity.

This current surge also presents an opportunity for people to begin to learn to live with higher case numbers so they will be better prepared mentally when China eventually does open up, said a member at a local branch of the CDC.

Beijing-based business manager Vivian Wang is among those already willing to risk exposure to Covid-19 in exchange for more freedom. On Sunday, she was ordered by building management staff to spend a Sunday night in her company’s office with three dozen other people without explanation, though she said suspects that a close contact of a Covid-19 patient had been in the same building.

“Nowadays I’m more worried about getting caught up in this kind of quarantine than catching the virus,” she said.

—Raffaele Huang contributed to this article.

Write to Sha Hua at sha.hua@wsj.com