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HONG KONG — The Hong Kong police fired rounds of tear gas and rubber bullets on Sunday to disperse protesters after some of them vandalized the Chinese government’s liaison office in the city, a direct challenge to Beijing’s authority after a peaceful protest earlier in the day.

In a separate clash, footage from a local television station showed, masked men, dressed in white and wielding sticks, assaulted antigovernment protesters in a train station late Sunday night in northwestern Hong Kong.

The unrest spiraled out of a march that called for an independent investigation into what protesters said was police brutality in earlier street clashes. The march was peaceful, but thousands of demonstrators later marched past where the police had said the official demonstration should end.

Protesters then occupied major roads and heckled police officers stationed outside government buildings. “Recover Hong Kong; it’s the time for revolution,” some chanted.

By nightfall, some protesters had defaced a crest of the Chinese government at the liaison office with eggs and black ink, and had sprayed the building’s exterior with graffiti.

Shortly after 8 p.m., about 100 riot police officers, some carrying guns with plastic rounds, approached the liaison office and dragged away metal barricades that protesters had placed in the road.

“Charge forward!” they shouted, as hundreds of protesters fled east through the streets.

Scuffles soon broke out nearby, with some protesters lobbing eggs and bags of liquid at the police during a standoff outside the Central Police Station. After a group of protesters charged forward and threw projectiles, riot police officers rushed them, shooting several rounds of tear gas.

That same evening, at the Yuen Long train station, an unknown group of masked men in white attacked protesters and civilians, said Jerming Zhang, a 16-year-old student and first-aid volunteer who was at the station.

He said in a phone interview that as civilians, including those with children, tried to flee the station, the masked men followed them onto an open train and continued beating people with wooden sticks.

“It was like a stampede,” he said. “They hit people indiscriminately, smiling as they beat them up.”

In a statement on Sunday night, the Hong Kong government condemned protesters who it said had “blatantly challenged the national sovereignty by maliciously besieging and storming” Beijing’s liaison office. It promised to “deal with these acts in a serious manner in accordance with the law.”

A later statement denounced the attack at the train station, saying “some people congregated at the platforms” and attacked and injured commuters. “This is absolutely unacceptable to Hong Kong as a society that observes the rule of law,” the statement said.

The Hong Kong and Macau Affairs Office of China’s State Council also condemned the actions of the protesters who blocked the liaison office and vandalized it, and warned of serious consequences.

“Such acts openly challenge the authority of the central government,” the statement said, calling the actions “absolutely intolerable.”

The developments on Sunday were the latest chapter in the city’s worst political crisis since China reclaimed sovereignty from Britain in 1997. They signaled growing antagonism between the largely peaceful protest movement and the front-line officers patrolling it.

“I hope that the police can take reasonable actions tonight,” Roy Kwong, a lawmaker who has been a driving force behind the protests, told reporters at the front lines early Sunday evening. “Otherwise, I fear that the anger of the people will erupt.”

The Civil Human Rights Front, which has helped organize the recent protests, said it estimated that 430,000 people had turned out for the officially sanctioned part of the march. A police spokeswoman said that the estimated number of people who had marched along the permitted route during the “peak period” was 138,000.

The police also said that they were investigating whether explosives found Friday at a “homemade laboratory” were related to the Sunday protest, but that they did not have enough evidence to make any conclusion. On Friday, the police said, officers seized about two pounds of powerful explosives, 10 gasoline bombs. and bullets and knives from an industrial building.

Three men in their 20s were arrested in connection with the case.

Hong Kong’s mass demonstrations began in early June in response to unpopular legislation that would have allowed extraditions to mainland China, where the courts are controlled by the governing Communist Party. The bill has since been suspended but not fully withdrawn, one of the protesters’ key demands.

On Sunday afternoon, thousands of protesters dressed mostly in black T-shirts set off on a march, some carrying signs saying, “No extradition to China” and “Stop police brutality.”

“The government must withdraw the bill and set up an independent inquiry committee to investigate the police,” said Tommy Tsang, an 81-year-old retiree.

He said he was particularly angered by the police violence. “If you don’t hit people, why would they hit you back?” he said.

Advisers to the territory’s embattled chief executive, Carrie Lam, say her administration did not intend to make further concessions to the protesters. That stance suggests the government is confident it can weather the protests, despite the risks of damage to the local economyor violence between demonstrators and police officers.

Police officials say that they have largely acted with restraint and have used force only when attacked by protesters. They accused some protesters of rioting during recent demonstrations, including one in which a small group forcefully stormed the Hong Kong legislature.

The police and a watchdog that monitors complaints against them have said they plan to investigate officers’ actions at a June 12 demonstration that turned violent. Many people in Hong Kong, a city of about seven million, say they believe that the police response that day — which included firing tear gas, rubber bullets and beanbag rounds — was excessive.

But the protesters and their supporters argue that the watchdog is not independent and will not conduct a fair investigation.

At the Sunday afternoon march, the crowd spanned a diverse age range. “Everyone is out here for their children,” said Sam Tam, 57, who attended marches this month with his 8-year-old daughter and about 18 relatives.

“The older generation has to say sorry to the younger generation for not listening to their voices,” he said.

As the sweltering day dragged on, it was mainly those from the core demographic of the recent protests — young people in their 20s — who occupied major roads and swelled outside government offices.

Brian Heung, a student at the University of Hong Kong, said he and other protesters had intentionally disobeyed the police out of a sense of desperation.

“We have done everything peacefully, and they don’t have a proper response,” Mr. Heung, 18, said after putting a Post-it note on a barricade outside Police Headquarters calling officers shameless. “So we had to push the limits.”

Thousands of protesters at the front of the crowd defied police orders and streamed west into Admiralty, the district that houses the city’s legislature. Some heckled police officers, while others gathered outside the Hong Kong Police Headquarters nearby, chanting, “Shame.”

Demonstrations in support of the police have also been organized by pro-establishment groups, including one on Saturday.