The unrest included attacks on the subway system and on businesses that protesters perceive to be supportive of Beijing. The police force said on Sunday that a protester had stabbed one of its officers in the neck, and that his condition was stable.

The rowdy gatherings on Sunday -coordinated via social media and encrypted messaging apps - highlighted the continuing opposition to the unpopular ban on wearing face masks and capped a momentous week in China’s relationship with the United States.

President Trump said on Friday that the two countries had reached an interim trade deal, offering a temporary détente in a rancorous dispute that has rattled investors, lawmakers and businesses.

Relations between China and the United States were further strained last weekend when a Houston Rockets executive’s post on Twitter supporting Hong Kong’s protest movement infuriated people on the Chinese mainland. Beijing initially fanned nationalistic outrage, but later moved to tamp down public anger at the N.B.A. amid concerns that it was damaging the country’s international reputation.

The demonstrations in Hong Kong on Sunday were varied, including smaller gatherings across the city, and also cases of vandalism and arson that targeted government offices, subway stations, and several banks and shops.

Some protesters blocked roads, broke streetlights, vandalized a train station and spray-painted antigovernment graffiti inside shopping malls.

The Hong Kong police said one of its officers had been slashed in the neck by a protester on Sunday evening with a “sharp-edged” object, and that two people were immediately arrested at the scene. Video of the incident circulating widely on social media appeared to show that the attack was unprovoked.

The police said the officer was conscious when he arrived at a hospital.

The South China Morning Post newspaper also reported that a man who protesters suspected being an undercover officer was attacked on Sunday in the Tseung Kwan O district, before other officers dispersed them.

China has increasingly depicted the protest movement in Hong Kong as being separatist in nature even though the demonstrators’ demands do not include a call for independence.

China’s top leader, Xi Jinping, in a meeting with the Nepalese prime minister on Sunday, delivered a stark warning against separatism that was likely targeted at advocates of Tibetan independence but could also be read as a signal to Hong Kong.

“Anyone attempting to split any part of China will only be ruined; any external force supporting the separation of China will only be regarded as a delusion by the Chinese people!” Mr. Xi was quoted as saying in a report by the official Xinhua News Agency.

Sunday’s unrest began suddenly in the afternoon, after a morning of relative calm in the city, and had been promoted on social media under the slogan “blossom everywhere.”

“The more widespread today’s operation is, the more difficult it is for the police to chase us down,” Andy Wong, a 19-year-old university student majoring in Chinese literature, said on the fringes of a flash-mob gathering in the Sha Tin district.

The police fired tear gas and made several arrests, and the city’s beleaguered subway operator closed more than two dozen stations. The entire train network had already been scheduled to close earlier than usual on Sunday night.

Some protesters said they were demonstrating this weekend to express continued opposition to the face-mask ban, which took effect last weekend and which makes covering one’s face at a public demonstration punishable by up to a year in prison. The city’s embattled leader, Carrie Lam, drew on rare emergency powers to invoke the ban this month, prompting a wave of violent protests across the city.

Other protesters said that they were disappointed in President Trump for telling reporters at the White House on Friday that Hong Kong’s protest movement had “toned down a lot from the initial days of a number of months ago” and would eventually ”take care of itself.”

“He only thinks about his interests, and he’s only seizing on Hong Kong to bargain with China,” Fanny Fung, a retiree who joined a demonstration in the Wan Chai district of Hong Kong on Saturday, said of Mr. Trump.

The protest movement began in June in opposition to contentious legislation, since shelved, that would have allowed extraditions from Hong Kong to the Chinese mainland, where the courts are controlled by the Communist Party. It has since expanded to include a wide range of demands for police accountability and greater democracy.

Many protesters in the movement have consistently appealed to the United States government for support. Notably, thousands marched to the United States Consulate in central Hong Kong last month to drum up support for a bill about the city that is moving through the American Congress.

The draft legislation would penalize officials in mainland China and Hong Kong who suppress freedoms in the city, and require an annual justification for why the United States should offer Hong Kong special trade and business privileges. It is scheduled to be considered on the House floor this week.

One of the bill’s vocal supporters in Congress, Senator Ted Cruz, Republican of Texas, traveled to Hong Kong this weekend and met with people in the protest movement. Mr. Cruz was scheduled to meet with Mrs. Lam, but he said on Saturday that she had scrapped the meeting after he refused her request to keep their conversation confidential - a claim that her office later denied.

The Hong Kong office of China’s Foreign Ministry said in a statement on Sunday night that Mr. Cruz had “lied through his teeth” and “made indiscreet remarks on Hong Kong affairs.”

Some of Sunday’s gatherings turned into tense standoffs between protesters and police officers. At one of them, a police officer briefly pointed a gun at protesters who were trying to block a main road into Sha Tin.

In a video circulating widely on Sunday afternoon, a masked protester is seen taking a flying leap to kick a riot officer, who was apparently trying to arrest another protester near a shopping center in the working-class Mong Kok neighborhood.

Protesters also vandalized a range of targets across the city on Sunday, including a Bank of China branch, offices of pro-Beijing political parties and at least two Starbucks.

Starbucks became a target for protesters when Annie Wu, the daughter of the founder of Maxim’s Group, a conglomerate that licenses the coffee chain in the city, called protesters “radical” in a September speech at the United Nations Human Rights Council in Geneva.

On Sunday, protesters broke into a shuttered Starbucks at a mall in the Tai Koo district and spray-painted “black heart” on its wooden countertop - a play on “beautiful heart,” a direct translation of the Maxim’s name in Chinese. Spokespeople for Starbucks and Maxim’s Group did not immediately return requests for comment.

Ben Chan, 47, who lives near the mall, said the vandalism didn’t bother or surprise him, and that he supported the young protesters behind it.

“Lots of people here support democracy,” he said. “The kids are well educated, and they fight for what they want.”

Reporting was contributed by Austin Ramzy and Elaine Yu from Hong Kong, and Edward Wong from Washington. Claire Fu contributed research from Beijing.