HONG KONG — A senior Hong Kong official on Monday warned for the first time that “elements of terror” were seen among the city’s pro-democracy protesters, as riot police officers took up positions around schools and spread out across Hong Kong’s subway system after a weekend of demonstrations punctuated by violence and vandalism.

The Hong Kong authorities had previously rejected a mainland official’s description of “signs of terrorism” in characterizing acts of violence by some protesters. But John Lee, the territory’s secretary for security, changed that stance on Monday, as the local government escalated its criticism of the monthslong demonstrations.

“The extent of violence, danger and destruction have reached very serious conditions,” Mr. Lee said. “Radical people have escalated their violent and illegal acts, showing elements of terror.”

Mr. Lee’s comments followed a weekend of intense protest. Tens of thousands of people defied a police ban and marched through several central neighborhoods on Saturday. Some clashed with riot police officers near the government headquarters, throwing rocks and firebombs as officers responded with tear gas, pepper spray and water cannon.

Monday was the start of the school year for many students in Hong Kong. Young people made up one of the largest groups of protesters in recent months, and their activism was likely to continue on campus, with strikes and demonstrations planned.

Despite a reasonably quiet day in the city, many students traveling to school on Monday passed riot police officers in subway stations and outside schools. It is a rare for officers to be in full riot armor when not responding directly to an active protest, and some students said they found the officers’ presence in peaceful areas intimidating.

“They are standing there and giving off the feeling that they want to catch the ‘black shirts’ and stop students from boycotting class,” said Queena Tung, a 17-year-old student.

Subway service was suspended across large parts of Hong Kong on Saturday because of clashes in stations, with three stations remaining closed for much of the next day.

On Sunday, demonstrators rallied outside Hong Kong International Airport, snarling transportation and shutting down train service to the transport hub, forcing travelers to scramble to get to and from the airport and overwhelming the bus system. A nearby subway station was also closed after it was damaged by protesters.

As a result, many protesters were forced to walk for hours to return to the city. Some crammed onto buses, while others were picked up by drivers who had volunteered to help with the exodus. The police waited in some subway stations and ferry terminals, looking for black T-shirts, the unofficial uniform of the protests, and other signs people had joined unauthorized assemblies.

Hong Kong’s chief secretary, Matthew Cheung, the city’s No. 2 official, gave his “strongest condemnation” of this weekend’s protests. “If violence is continuing we must stop it, without further ado. No nonsense,” he said. “Society must go back to normal.”

Mr. Lee also criticized members of the public who supported the more extreme protesters.

“Rationalizing or tolerating these serious acts of violence will turn into approving of violence and encouraging violence, making the violence spread, pushing Hong Kong to the brink of malfunctioning,” he said. “Yet in society there are instances where society acquiesces to violence. So I urge Hong Kong civilians to collectively say no to violence, and safeguard Hong Kong’s order and rule of law.”

The protests began over a government proposal, since suspended, that would have allowed extraditions to mainland China. Hong Kong, a former British colony, returned to Chinese control in 1997 under a “one country, two systems” model, with far greater civil rights protections than mainland China. But many people felt the extradition plan would undermine that.

The protesters’ demands have since grown to include an independent investigation into the police use of force, amnesty for arrested protesters and expanded direct elections.

So far, China’s leaders have not commented publicly on the violence over the weekend. Mainland Chinese media, though, warned the protesters that the central government would not back down. On Sunday, People’s Daily, the main newspaper of the Chinese Communist Party, said that the Hong Kong police were entirely justified in using force against the protesters.

“These rioters would be well advised that it would be childish to underestimate the capacity of the police to halt violence,” the paper said in an online article. “Standing by them are 7 million Hong Kong residents, and the ‘police support squad’ of 1.4 billion Chinese people.”

Xinhua, China’s main state news agency, said the weekend mayhem proved that the protesters were determined to push Hong Kong into chaos, as part of what it said was a strategy of “color revolution” — the party’s term for Western-backed insurrection.

“Their true intentions are increasingly clear,” Xinhua said on Sunday. “By fomenting turmoil in Hong Kong, they are attempting to seize power from the special administrative region, to smash ‘one country, two systems,’ and infiltrate ‘color revolution’ into the Chinese mainland.”

Chris Buckley, Tiffany May and Elaine Yu contributed reporting from Hong Kong.

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