“Xi’s leadership is in a bind,” said

Yuen Yuen Ang,

a political scientist focused on China at the University of Michigan. “If they compromise and relax zero-Covid, they fear it will encourage mass protests. If they repress more, it will create wider and deeper grievances.”

Protesters across China have directly challenged the authority of the Chinese leader and the Communist Party in scenes unthinkable just a month ago, when Mr. Xi secured a third term in power.

In Shanghai over the weekend, protesters used call-and-response chanting to demand political change. In Beijing, crowds shouted “Freedom.” In other large cities, demonstrators marched holding blank sheets of paper—a swipe at government censorship.

China experts say the protests are unlikely to translate into a leadership change, in the near term at least. But Beijing’s dilemma is a tough one. It could lift restrictions and risk a large and potentially deadly wave of Covid infections that could undermine its credibility. Or it could crack down on the demonstrators and stick with a strict pandemic strategy that large parts of the population are clearly fed up with.

All three benchmark U.S. stock indexes closed more than 1% lower on Monday as investors worried that the protests would lead to more market volatility.

Widespread and public outpourings of political grievance have been extremely rare in a country where people have long consented to obey party authorities—as long as they deliver prosperity and allow citizens relative freedom in their personal lives.

The protests put in stark relief the fraying of that social contract, showing that the climbing economic and social costs of China’s zero-Covid policies—coupled with an increasingly authoritarian regime’s zero-tolerance for dissent—have driven many to a kind of breaking point.

Demonstrations aren’t unusual in China, but they are largely over local grievances such as unpaid wages, land disputes or pollution. Since the Tiananmen Square protests in 1989, the party has made it a priority to prevent nationwide protests of a political nature.

The current wave of unrest started last week in the remote northwestern region of Xinjiang after 10 people died in a fire. Residents contended that Covid restrictions were partly to blame for delaying rescuers and contributing to the death toll. Officials said some barriers had to be moved but attributed the delay to parked cars in the way.

In the days since, the anger has spread across China. On Monday, authorities moved broadly to prevent any new protests, including dozens of uniformed and undercover police swarming the area around a highway bridge in Beijing where a lone protester hung a banner denouncing Mr. Xi in October. On Sunday, protesters had chanted lines from the banners.

The unrest also underlined how anger about the Covid restrictions has united people from a range of social backgrounds—from migrant workers assembling iPhones in central China and residents of the remote region of Xinjiang to college students and middle-class urbanites in the nation’s biggest cities.

“The mass protests represent the biggest political crisis for Xi,” said

Minxin Pei,

editor of quarterly academic journal China Leadership Monitor. “It’s the first time in recent decades that protesters from a broad coalition of social groups have mounted a direct challenge to both the top leader himself and the party.”

Sudden reopening could lead to millions of intensive-care admissions in a country with fewer than four ICU beds per 100,000 people, and where many elderly still haven’t been fully vaccinated, according to public-health experts and official data. In addition, such a compromise would send a signal to the general public that mass protests are an effective means to win change, not something the government would want to encourage.

On the other hand, sticking to the zero-Covid policy could stir up even greater public resentment toward the leadership, with hard-to-gauge consequences.

The University of Michigan’s Ms. Ang and others say that the protests are unlikely to lead to any radical policy shift. Rather, one likely outcome is a mixture of selective relaxation of controls and harsh retaliation against select protesters.

“The danger is that if the leadership responds with repression, that could take China down a vicious cycle of control, leading to more grievances, to more control,” Ms. Ang said.

China’s Covid struggle underscores the limits of a political system where a lack of public debate has made it hard to adjust policies as other countries have done.

Many public-health experts say Beijing has missed the window to put in place a gradual exit plan out of zero-Covid. For the past three years, the government has spent significant resources on building ever more quarantine facilities and expanding mass-testing capabilities, while China’s progress on developing more effective vaccines has been slow.

Partly thanks to Beijing’s early successes at stemming infections, the Chinese population has developed little natural immunity. It only has access to homegrown vaccines that are less effective than some of the global alternatives.

Notably, negotiations between China and the European Union over mRNA vaccine imports from the bloc fell through nearly two years ago, according to people familiar with the matter, after Beijing insisted that Europe recognize Chinese vaccines.

Beijing has also resisted approving any large-scale adoption of the mRNA vaccine co-developed by

Pfizer Inc.

and

BioNTech SE,

a decision healthcare and foreign-policy experts attribute partly to China’s strained relations with the U.S.

Mr. Xi and the party have faced public anger before, most notably during the early days of the pandemic when emotions swelled with the death from the virus of

Li Wenliang,

a young doctor in the city of Wuhan who was punished for trying to raise an early alarm. Ultimately, much of the nation’s anger then was directed at local authorities.

In the years since, Mr. Xi has identified himself closely with the zero-Covid strategy. That is now turning him into the natural target of protesters’ fury and has also made it nearly impossible to shift course without diminishing his standing. Notably, a People’s Daily article on Sunday continued to stress the importance of unwaveringly sticking to the existing Covid-control policy.

As repeated lockdowns kept businesses closed and pushed up unemployment, some hoped there would be a shift away from the zero-Covid strategy once an October party conclave that handed Mr. Xi another five-year term was over.

As long as the top leader felt politically secure enough, those people argued, he would want to adjust the policy to help the economy—which still matters to the leadership despite its increased emphasis on ideology and party control.

Businesses and investors alike cheered when Beijing earlier this month unveiled plans to “optimize and adjust” the Covid policy, including shortened quarantine restrictions. Many market analysts viewed the step as the beginning of a gradual exit from zero-Covid.

However, as Covid cases surged again along with the colder season, local officials across the country reimposed strict restrictions for fear of putting their jobs in jeopardy. Keeping Covid under control has remained the overarching political priority for localities that are also struggling to reboot economic activity.

The contrast of China’s continued Covid lockdowns as the rest of the world has moved on became more obvious over the past week as many Chinese soccer fans have seen TV images of thousands of maskless spectators cheering in stadiums during the World Cup in Qatar.

Then came the deadly fire in Urumqi, the capital of Xinjiang, where residents had struggled with lockdowns of more than 100 days, prompting protesters across the country to defy the risks of expressing dissent to seek change.

Write to Lingling Wei at Lingling.Wei@wsj.com