On Sunday, a protester stabbed a police officer in the neck, the authorities said. In a separate incident on the same day, a homemade bomb was detonated, though it did not injure anyone.
The state-run media in China have repeatedly denounced the demonstrators as rioters who are working on behalf of foreign governments to bring about a revolution in China. The country’s leader, Xi Jinping, delivered a harsh warning against separatism on Sunday, though he did not specifically mention Hong Kong.
“Anyone attempting to split any part of China will only be ruined,” Mr. Xi said.
Tensions are likely to rise further ahead of elections in November to choose members of Hong Kong’s district councils. Pro-democracy activists worry that the government may try to disqualify candidates who have taken part in the protests on the grounds that they are separatists.
Victoria Hui, an associate professor who studies Hong Kong politics at the University of Notre Dame, said that it would be difficult for Mrs. Lam to quell the protests by vowing to tackle inequality. She said many residents are skeptical of promises by the government because it allowed Hong Kong’s social and economic problems to fester for years.
“The problems are so intractable,” Ms. Hui said. “Even if she can perform a miracle, it will be difficult to gain the trust of the public.”
Reporting was contribute by Tiffany May, Elaine Yu and Ezra Cheung.