China has accused protesters who vandalised Hong Kong's parliament on Monday of "serious illegal actions" that "trample on the rule of law".

A group of activists occupied the Legislative Council (LegCo) building for several hours after breaking away from a peaceful protest.

Hundreds of police used tear gas to disperse demonstrators.

The Chinese government urged the city to investigate the "criminal responsibility of violent offenders".

Hong Kong, a former British colony, is part of China but run under a "one country, two systems" arrangement that guarantees it a level of autonomy. Its citizens enjoy rights not seen on the mainland.

Monday's disorder followed weeks of mass protests over a controversial extradition bill, which critics have said could be used to send political dissidents from Hong Kong to the mainland.

The Chinese government said the ransacking of parliament was a blatant challenge to the "one country, two systems" formula.

So far, Beijing has reacted to the protests from a distance, but Monday's violence could be a catalyst for Beijing to push for tighter control over Hong Kong, says BBC World Service Asia-Pacific editor Celia Hatton.

Hong Kong's leader Carrie Lam earlier made similar remarks, condemning the "extreme use of violence" by the protesters who had broken into LegCo.

"Nothing is more important than the rule of law in Hong Kong," she told a pre-dawn press conference on Tuesday, flanked by Police Commissioner Lo Wai-chung.

The government suspended the extradition bill last month and it is now unlikely to pass, but the protesters want it scrapped completely and are calling on Ms Lam to stand down.

What happened on Monday?

The anniversary of Hong Kong's handover from British to Chinese rule in 1997 is marked by an annual pro-democracy march, but this year's event had been expected to be larger than usual.

There were some scuffles in the early morning, as protesters blocked streets around the venue where Ms Lam was attending the annual flag-raising ceremony.

At around midday, hundreds of demonstrators broke off from the main protest and made their way to LegCo.

The protesters see Ms Lam as doing Beijing's bidding

They effectively besieged the building before eventually smashing their way through the glass facade.

Inside, they defaced the emblem of Hong Kong in the central chamber, raised the old British colonial flag, spray-painted messages across the walls and shattered furniture.

They gradually left the building amid warnings of an impending police clearance operation.

At about midnight outside the building, protesters clad in plastic helmets and brandishing umbrellas retreated from a baton charge by riot police, who quickly overcame their makeshift barriers.

Within an hour, the streets around the building were clear of everyone except the media and police.

What did Carrie Lam say?

She said it was a scene that "really saddens... and shocks a lot of people".

The annual peaceful march on 1 July, by contrast, reflected "the core values we attach to peace and order" in Hong Kong.

Showing little emotion, she said she hoped society would "return to normal as soon as possible".

She strongly denied she could be blamed for failing to address the protesters' demands, saying the government had "not responded to every demand asked because of good reasons".

The extradition bill would now expire with the end of the government's term, she said. "That is a very positive response to the demands that we have heard."

She also argued that granting an amnesty to all protesters would not be "in accordance with the rule of law".

Ms Lam added that Hong Kong's authorities would "pursue any illegal acts" carried out by demonstrators.

Why are people protesting?

Protests began in June, focusing on the extradition law. But demonstrators have now broadened their demands to include the release of all detained activists, and investigations into alleged police violence.

They have also expressed general concerns over Beijing's influence eroding the territory's rule of law and special rights.

Many protesters have said they will not back down until all their demands are met.

Other countries have been reacting to the unrest in Hong Kong:

• Before Monday's protests erupted into violence, US President Donald Trump expressed his support for the protesters, saying they were "looking for democracy" and "unfortunately, some governments don't want democracy".

• UK Foreign Secretary Jeremy Hunt said Britain condemned "violence on all sides" but called on the authorities to "understand the root causes of what happened, which is a deep seated concern by people in Hong Kong that their basic freedoms are under attack"

• Taiwanese Foreign Minister Joseph Wu said the people of Hong Kong were "seething with anger and frustration" and the idea of "one country, two systems" was "nothing but a lie"