HONG KONG — With her city facing an abyss, in her words, Hong Kong leader Carrie Lam strode to the microphone this week and reasserted that urgent steps were needed to pacify protests that have plunged the Asian financial hub into its worst crisis in decades.

What she must not do, she said, is compromise. She wasn’t ignoring protesters’ demands, she said. She was rejecting them outright.

“It is not a question of not responding; it is a question of not accepting those demands,” she said.

As Hong Kong’s political upheaval stretches on, the refusal of Lam and her government to entertain any concessions that might restore calm has surprised even pro-establishment voices and moderates. Her stance has left many wondering whether Lam is unable — rather than unwilling — to make decisions on the most pressing matters affecting the semiautonomous Chinese territory.

“Beijing thinks the protests will burn out as a result of the regime’s intransigence and provocations,” said Kenneth Chan, a political science professor at Hong Kong Baptist University and a former pro-democracy lawmaker. “The ultimate game is to imbue in society a collective sense of hopelessness [by] stonewalling the protests.”

Lam’s office, in response to a request to elaborate on her Tuesday remarks, said her government has responded to protesters, particularly by stopping work on the extradition bill that sparked the unrest. It said it hoped that dialogue with “people from all walks of life, including those with different political views,” would help address differences.

Two years into her term as chief executive, Lam, a former civil servant, is under immense pressure to ease tensions in Hong Kong. Tourists are canceling trips, forcing hotels to put staff on unpaid leave. Businesses are hurting; some are sharpening exit plans. Residents have become casualties of tear gas. More strikes and protests are planned in the coming days.

China’s ruling Communist Party has issued ominous threats to try to stamp out the protests. On Thursday, the People’s Liberation Army conducted its 22nd troop rotation into the Hong Kong garrison since 1997, state media said. Pictures showed armored personnel carriers moving between the border city of Shenzhen and Hong Kong, underscoring fears of a Chinese military intervention. The paramilitary People’s Armed Police have been practicing crowd-control tactics at a Shenzhen stadium in recent weeks.

And, in a widening crackdown, activists Joshua Wong and Agnes Chow, student leaders who rose to prominence in pro-democracy street protests five years ago, were arrested Friday morning, their party said in a statement.

With the crisis threatening to tip Hong Kong into recession and public grievances playing out in street clashes with police, there is little indication that Lam intends to give ground. Whether she has the authority to do so, political analysts say, is central to Hong Kong’s status and its ability to exercise a “high degree of autonomy,” to which the city is entitled under the terms of its 1997 return to Chinese sovereignty. Lam, who is appointed by a committee mostly loyal to Beijing rather than by popular vote, said Tuesday that she had not lost control.

“I don’t think people even wonder anymore who is in charge,” said one business executive in Hong Kong, speaking on the condition of anonymity because of the political sensitivity. Hong Kong’s government has offered “nothing” by way of explanation to the business community on why it won’t make concessions, the executive said.

Regina Ip, a member of Hong Kong’s Executive Council and a pro-Beijing lawmaker, said top leaders are “united” behind Lam and her decision.

Hardcore demonstrators “are finding every conceivable excuse to stage more protests,” she said in an interview. “That’s why I really wonder if giving in to any of their demands will stop their protests.”

Lam has tried to kick-start a “platform for dialogue,” hoping to get protesters to talk with her government. At her residence Saturday, Lam held the first meeting aimed at establishing this platform, attended by 19 politically moderate local luminaries.

More than half the people in attendance, one participant told The Washington Post, were in favor of addressing two key protester demands: complete withdrawal of the extradition bill that triggered the protests and an independent investigation that would include scrutiny of police tactics. Lam has suspended the bill, which would have allowed Hong Kong to extradite criminal suspects to mainland China, but has stopped short of withdrawing it from the legislative agenda.

At the Saturday meeting, Lam appeared to understand that fully withdrawing the bill would be effective in easing tensions, but she was more resistant to protesters’ calls for an independent inquiry into the months of violence for fear of aggravating the police force, said Tik Chi-yuen, chairman of the centrist political group Third Side, who was present. Police have said that an existing internal mechanism for investigating complaints is sufficient.

Given her “soft approach” in the weekend meeting, Tik said he was surprised when Lam, in her news conference just days later, appeared to flatly reject the idea of meeting any of the protesters’ five demands.

Efforts to start a dialogue without concessions would be “meaningless” and “not effective,” Tik said. “You cannot achieve anything.”

Raymond Mak, a former member of the Path of Democracy think tank who also attended Saturday’s meeting, said Lam listened attentively but was noncommittal on proposals raised. “Everyone expects that for meaningful dialogue, the government should come up with a concrete proposal because otherwise the dialogue is going nowhere,” he said.

Lam’s refusal to budge has perplexed even some in her own camp.

“There’s a consensus that the government can do two things, but she refuses to do anything,” said Felix Chung, a pro-Beijing lawmaker who also represents the textiles and garment industry.

Senior government officials, he added, have urged her to start work on an independent inquiry and formally withdraw the bill. “It is very difficult to have anything done at this moment if she still insists on not doing anything simple.”

Surveys show that Lam may have limited ability to connect with the majority in her city. An August survey released this week by the Hong Kong Public Opinion Research Program, an independent pollster, put Lam’s approval rating at 24.6 percent — the lowest among any post-colonial leader. Net trust in the Hong Kong government is also at its lowest since records began in 1992.

Lam has other options to end the crisis. The pro-government Sing Tao Daily newspaper floated the idea of invoking the colonial-era Emergency Regulations Ordinance, which grants sweeping powers to the chief executive.

Lam on Tuesday did not dismiss the idea, saying that the government would look into all Hong Kong laws that could “stop violence and chaos.” This month, she asked at a news conference whether protesters “really want to push [Hong Kong] into an abyss.”

Under the law, the chief executive is granted control over detentions and deportations, arrests and transportation hubs, as well as the ability to censor publications. The ordinance was used in 1967 during leftist riots in which 51 people were killed and nearly 900 injured.

The discussion on resorting to emergency legislation is “a highly contentious if not dangerous move” that will have an “immediate and profound impact on Hong Kong’s reputation as a free society and rule of law,” said Peter ­Cheung, a political scientist at the Education University of Hong Kong.

In private meetings, Lam has expressed optimism that protests will die down once school reopens next month. Yet students are planning a mass boycott of classes, and protest organizing is fervent ahead of the 70th anniversary of the founding of the People’s Republic of China in October.

Lam “wants to arrest everyone or wants for the movement to die down. It is not going to happen,” said Bonnie Leung, one of the leaders of the Civil Human Rights Front, which organized some of the biggest protest marches. The group has planned a rally for Saturday, but police have declined to authorize it.

Chung, the pro-Beijing lawmaker, added: “How do you expect the protesters or the rioters to stop it without any response from the government? Don’t be naive.”

Some pro-establishment Hong Kong lawmakers have pleaded with Beijing for compromise, fearing a deepening and growing mistrust between Hong Kong’s police and citizens. Michael Tien, a Hong Kong delegate to the Communist Party’s National People’s Congress in Beijing, in a previous interview said Chinese officials have given the Hong Kong government “no more room to move.”

Even those who met with Lam over the weekend suspected she wasn’t the one they needed to be talking to.

“She cannot say the whole picture to us,” said Tik from Third Side. “What is behind it? I don’t know. We can speculate that Beijing is an issue.”