China also lashed out at the UK's foreign secretary, Dominic Raab, after he spoke to Ms Lam about the protests and called for a "fully independent investigation" to rebuild trust. "It is simply wrong for the British government to directly call Hong Kong's chief executive to exert pressure," said a spokeswoman for China's foreign ministry.
After Cathay staff took part in demonstrations, the Chinese state-owned English-language Global Times warned last week that the company would "pay a painful price".
China's Civil Aviation Administration said in a statement on Friday that Cathay's failure to take action "gravely threatened aviation safety, created negative social consequences and increased the risk of flying from Hong Kong to mainland China".
The regulator also called on the airline to submit identification details of all crews flying to China or over Chinese airspace.
On Saturday night Cathay confirmed it had fired two airport ground staff for "misconduct". Earlier the company said it was "aware of the inappropriate behaviour of an employee involving the misuse of company information" after a Cathay staffer was accused by Chinese state media of posting on social media about a group of Hong Kong police officers travelling on the airline.
The company also suspended a pilot who faces rioting charges from the Hong Kong protests.
Cathay said in a message to staff it would report to China's aviation regulator before midnight on August 15 on "action taken to step up internal safety controls".
Cathay's principal shareholder is Swire Pacific, the Hong Kong-listed arm of the Swire Group, a London and Hong Kong-based conglomerate with a history stretching back into the territory's colonial era. Beijing's flag carrier Air China is another major shareholder.
Online postings by mainland residents indicate that anger is growing towards the Hong Kong demonstrators and businesses that are perceived by Beijing as tacitly supporting them.
Beijing has ratcheted up its rhetoric as it faces the worst political crisis in Hong Kong since the territory transferred from British to Chinese rule in 1997.
Under the deal given to Hong Kong after the handover, residents were granted civic liberties including freedom of expression.
Cathay is bracing for more pain, cautioning last week that the airline had seen a drop off in inbound flight bookings to Hong Kong. The economic fallout of the protests is being felt widely, with the government warning the territory risks falling into a technical recession next quarter.
Copyright The Financial Times Limited 2019