* Police fire tear gas to try to clear protesters from legislature

* Anger over extradition bill coincides with handover rally

* Protests pose big challenge for Chinese leader Xi Jinping

* Major roads in heart of financial centre paralysed

By John Ruwitch and Joyce Zhou

HONG KONG, July 1 (Reuters) - Hong Kong police fired tear gas to try to disperse hundreds of protesters, some of whom stormed the legislature, destroyed pictures and daubed walls with graffiti, on the anniversary of the city's 1997 return to Chinese rule on Monday.

Police arrived by bus and ran into position as about a thousand protesters gathered around the Legislative Council building in the heart of the former British colony's financial district.

Police fired several rounds of tear gas as protesters held up umbrellas to protect themselves or fled. Plumes of smoke billowed across major thoroughfares and in between some of the world's tallest skyscrapers.

Protesters had carried road signs, others corrugated iron sheets and pieces of scaffolding, as they barged into the council building. Some sat at legislators' desks, checking their phones, while others scrawled "anti-extradition" on chamber walls.

Other graffiti called for Hong Kong leader Carrie Lam to step down, while pictures of some lawmakers were defaced.

"HK Is Not China" was painted in black on a white pillar.

The government called for an immediate end to the violence, saying it had stopped all work on extradition bill amendments and that the legislation would automatically lapse in July next year.

A small group of mostly students wearing hard hats and masks had used a metal trolley, poles and scaffolding to charge again and again at the compound's reinforced glass doors, which eventually gave.

The Legislative Council Secretariat released a statement cancelling business for Tuesday. The central government offices said they would close on Tuesday "owing to security consideration", while all guided tours to the Legislative Council complex were suspended until further notice.

Riot police in helmets and carrying batons earlier fired pepper spray as the standoff continued into the sweltering heat of the evening. Some demonstrators removed steel bars that were reinforcing parts of the council building.

Banners hanging over flyovers at the protest site read: "Free Hong Kong."

The protesters, some with cling film wrapped around their arms to protect them from tear gas, once again paralysed parts of the Asian financial hub as they occupied roads after blocking them off with metal barriers.

Lam suspended the extradition bill on June 15 after some of the largest and most violent protests in the city in decades, but stopped short of protesters' demands to scrap it.

It was not immediately clear if the announcement that it would lapse would ease the tension.

The Beijing-backed leader is now clinging on to her job at a time of an unprecedented backlash against the government that poses the greatest popular challenge to Chinese leader Xi Jinping since he came to power in 2012.

"The kind of deafness that I see in the government this time around despite these protests is really worrying. The complete disregard for the will of the people is what alarms me," said Steve, a British lawyer who has worked in Hong Kong for 30 years.

"If this bill is not completely scrapped, I will have no choice but to leave my home, Hong Kong."

Opponents of the extradition bill, which would allow people to be sent to mainland China for trial in courts controlled by the Communist Party, fear it is a threat to Hong Kong's much-cherished rule of law.

Hong Kong returned to China under a "one country, two systems" formula that allows freedoms not enjoyed in mainland China, including freedom to protest and an independent judiciary.

Beijing denies interfering but, for many Hong Kong residents, the extradition bill is the latest step in a relentless march towards mainland control.

China has been angered by criticism from Western capitals, including Washington and London, about the legislation. Beijing said on Monday that Britain had no responsibility for Hong Kong any more and was opposed to its "gesticulating" about the territory.

The European Union on Monday called for restraint and dialogue to find a way forward.

THOUSANDS RALLY

Tens of thousands marched in temperatures of around 33 degrees Celsius (91.4°F) from Victoria Park in an annual rally. Many clapped as protesters held up a poster of Lam inside a bamboo cage. Organisers said 550,000 turned out. Police said there were 190,000 at their peak.

More than a million people have taken to the streets at times over the past three weeks to vent their anger.

A tired-looking Lam appeared in public for the first time in nearly two weeks, before the storming of the legislature, flanked by her husband and former Hong Kong leader Tung Chee-hwa.

"The incident that happened in recent months has led to controversies and disputes between the public and the government," she said. "This has made me fully realise that I, as a politician, have to remind myself all the time of the need to grasp public sentiment accurately."

Pro-democracy lawmakers and the protest organiser said Lam has ignored the demands of the people and pushed youngsters towards desperation, despite pledging to listen to people's demands.

PROTEST MOVEMENT REINVIGORATED

Beijing's grip over Hong Kong has intensified markedly since Xi took power and after pro-democracy street protests that gripped the city in 2014 but failed to wrestle concessions from China.

Tensions spiralled on June 12 when police fired rubber bullets and tear gas at protesters near the heart of the city.

The uproar has reignited a protest movement that had lost steam after the failed 2014 demonstrations that led to the arrests of hundreds.

The turmoil comes at a delicate time for Beijing, which is grappling with a trade dispute with the United States, a faltering economy and tensions in the South China Sea.

The extradition bill has also spooked some Hong Kong tycoons into starting to move their personal wealth offshore, according to financial advisers familiar with the details. (Additional reporting by Reuters TV, David Lague, Sumeet Chatterjee, Alun John, Vimvam Tong, Thomas Peter, Jessie Pang, Felix Tam, Sharon Lam, Donny Kwok, Joyce Zhou and Twinnie Siu in HONG KONG, Ben Blanchard in BEIJING and Foo Yun Chee in BRUSSELS; Writing by Anne Marie Roantree; Editing by Nick Macfie)

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