* Business very worried about protests -Lam
* China issues air safety alert after Cathay staff join protests
* Lam refuses demands for inquiry into police behaviour
* Thousands protest at Hong Kong airport, more planned (Adds safety alert on Cathay Pacific)
By Noah Sin and Clare Jim
HONG KONG, Aug 9 (Reuters) - Hong Kong's protests are hitting its economy, the city's leader Carrie Lam said on Friday, echoing warnings from business leaders including powerful local property developers, as about 1,000 mostly young activists occupied the airport arrivals hall.
China, whose rule over the city is being challenged by the protests, meanwhile demanded Hong Kong flag carrier Cathay Pacific Airways suspend staff involved in the demonstrations. One of its pilots was arrested last week.
The pair of warnings -- one aimed at residents planning more marches still and the other at a business emblematic of the city's colonial past -- mark a toughening stance by authorities as they grapple with Hong Kong's deepest crisis in decades.
Flanked by business leaders, Chief Executive Lam told reporters that companies in the Asian financial hub were "very worried" about the economic fallout from the protests, which began in June and have become increasingly violent.
"We have had two months of political dispute," she said after meeting business representatives and senior officials, warning that a downturn "is coming very quickly".
"Some people have described it as coming like a tsunami ... the economic recovery will take a long time," Lam said.
What started as an angry response to a now-suspended measure for criminal suspects to be extradited for trial in China has rapidly broadened to encompass calls for more democracy, Lam's resignation, and even keeping out mainland tourists.
The protests represent a populist challenge to Chinese leader Xi Jinping, just as an escalating trade war between China and the United States also hammers Hong Kong's economy.
China's warning on Cathay, saying crew who engaged in the protests pose a threat to safety and should be suspended from staffing flights to the mainland, follows the pilot's arrest and tumbling bookings.
Cathay has said it is taking the directive seriously, though when asked about staff participating in protests last week, Chairman John Slosar said the company "wouldn't dream" of telling staff "what to think about something".
Dozens of other Hong Kong companies have warned of faltering earnings, while city officials caution daily that the protests are hurting livelihoods and could help trigger a recession.
Lam said the city's Executive Council would next week resume meetings suspended in mid-June to prepare a policy response that would consider "daring measures".
"For Hong Kong's society to recover the foundation is the same (as that of the economy)," she said. "We must stop the widespread violence."
She urged landlords to ease rents on hard-pressed retailers, but dismissed demands for an inquiry into police behaviour at demonstrations.
"I disagree with (establishing) an independent inquiry that targets police work," she said. "I don't think we should just sort of make concessions in order to silence the violent protesters."
Young people have been at the forefront of the protests, worried about China encroaching on Hong Kong's freedoms but also concerned with issues such as sky-high living costs and what many see as an unfair housing policy favouring the wealthy.
Soaring property prices have pushed up rents and had a knock-on effect on prices of goods and services. Last year, Oxfam said the city's income inequality was at its highest in more than four decades.
Hong Kong's property developers spoke out for the first time on Friday, urging calm in a statement signed by 17 companies, including CK Asset Holdings Ltd, founded by property tycoon Li Ka-shing, the city's richest man.
At the airport, protesters sang "Do You Hear the People Sing?" from the musical "Les Miserables" and chanted: "Democracy now" and "Hong Kongers, add oil!" — a popular exhortation in Cantonese.
There was no visible police presence. Seeking to engage tourists, activists handed out anti-government leaflets and waved banners in a dozen languages.
"It will be a peaceful protest as long as the police do not show up," Charlotte Lam, 16, told Reuters.
"We have made stickers, banners in over 16 languages, ranging from Japanese to Spanish. We want to spread our message internationally. We are not rioters, we are a group of Hong Kong people fighting for human rights and freedom."
Marches are planned across Hong Kong, Kowloon and the New Territories over the weekend, where protesters could see a shift in police tactics.
To help deal with the protests, Hong Kong has recalled from retirement a police commander who oversaw the response to pro-democracy demonstrations in 2014.
Alan Lau Yip-shing will handle large public events, including activities to mark the 70th anniversary of the founding of the People's Republic of China on Oct. 1, the government said in a statement.
The escalating violence has already prompted travel warnings from countries including the United States and Australia, although the airport demonstration did not prompt complaints.
"I don't really know what to think about the protest," said Joyce, a New Zealander.
"Right now I just hope it won't delay my flight. But at the same time, as long as you're making a point without making too much trouble, it's OK." (Reporting By Anne Marie Roantree, Noah Sin, Donny Kwok, Clare Jim, Felix Tam, Lukas Job and Farah Master; Writing by Tom Westbrook; Editing by Darren Schuettler, Clarence Fernandez and Catherine Evans)