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* Carrie Lam defiant during news briefing
* Airport reopens, braces for more demonstrations
* Protests post major challenge to Hong Kong and Chinese rule
* Protesters fill airport, stock market falls (Recasts with fresh quotes and context)
HONG KONG, Aug 13 (Reuters) - A state of "panic and chaos" exists in Hong Kong, the city's embattled leader said on Tuesday, defying calls to quit as the stock market tumbled, airlines flagged further flight disruptions and anti-government protesters filled the airport.
Unrest has roiled the former British colony for 10 weeks this summer, as thousands of residents chafe at a perceived erosion of freedoms and autonomy under Chinese rule.
The increasingly violent demonstrations have plunged the Asian financial hub into its most serious crisis in decades, presenting Chinese leader Xi Jinping with one of his biggest challenges since he came to power in 2012.
For a fifth day, protesters occupied the arrivals hall at the airport, shut down in an unprecedented move on Monday that forced hundreds of flight cancellations. Beijing likened the demonstrations in Hong Kong to terrorism.
"Take a minute to look at our city, our home," Chief Executive Carrie Lam told a news conference at the government headquarters complex, fortified with 6-foot (1.8m) high water-filled barricades.
"Can we bear to push it into the abyss and see it smashed to pieces?" she added, her voice wavering.
As she spoke, the benchmark Hang Seng index hit a seven-month low. By lunchtime, it had dropped nearly 2%, dragging down markets across Asia. It has fallen 6% since the protests began in June.
The protests began as opposition to a now-suspended bill that would have allowed extradition to mainland China for those facing criminal charges, but have swelled into wider calls for democracy.
Demonstrators say they are fighting the erosion of the "one country, two systems" arrangement enshrining some autonomy for Hong Kong when China took it back from Britain in 1997.
They want Lam to resign. She said she would stay.
"My responsibility goes beyond this particular range of protest," she said, adding that violence had pushed the territory into a state of "panic and chaos".
"I, as the chief executive, will be responsible to rebuild the Hong Kong economy, to engage as widely as possible, listen as attentively as possible to my people's grievances and try to help Hong Kong to move on."
She did not respond to repeated requests to clarify if she had the power to withdraw the extradition bill to satisfy a key demand by protesters, or if she required Beijing's approval.
On Monday China said the protests had reached a critical juncture, after a weekend of street clashes in which both police and protesters appeared to toughen their resolve.
Police fired tear gas at the black-shirted crowds in districts on Hong Kong island, Kowloon and the New Territories.
A senior Chinese official said "sprouts of terrorism" were emerging in Hong Kong, given instances of violent attacks against police officers.
Hong Kong legal experts say Beijing might be paving the way to use anti-terror laws to restrain the protesters.
Some flights resumed as Hong Kong's airport reopened on Tuesday, but hundreds remained cancelled.
Airport officials said they aimed to resume normal service in the afternoon, but warned of further protests as the atmosphere at the airport grew more confrontational.
"Sorry for the inconvenience, we are fighting for the future of our home," read a banner held by some of the hundreds of protesters who had returned to the arrivals hall.
Some passengers challenged protesters over the delays as tempers began to fray, while the demonstrators, employing a Chinese term of encouragement, chanted, "Hong Kong people - add oil!"
Flag carrier Cathay Pacific urged passengers to postpone non-essential travel on Tuesday and Wednesday.
The airline, whose British heritage makes it symbol of Hong Kong's colonial past, is also in a political bind.
China's civil aviation regulator demanded it suspend personnel who joined or backed the protests from flights into its airspace, pushing its shares to a 10-year low on Monday and lower still on Tuesday.
The airport closure added to that pressure, though some firms benefited from the chaos.
Shares in Shenzhen Airport Co Ltd surged 10%, the maximum allowed on the index, buoyed by potential flight diversions.
Flagship carrier Air China said it would add capacity on its Beijing-Shenzhen route, as a result of the disruptions.
Other Chinese airlines have offered passengers a free switch of destination from Hong Kong to nearby locations such as Guangzhou, Macau, Shenzhen or Zhuhai. (Additional reporting by Felix Tam, Noah Sin, Donny Kwok, Greg Torode and James Pomfret in HONG KONG; Additional reporting by Jamie Freed in SINGAPORE and Stella Qiu in BEIJING. Editing by)