Hong Kong’s chief executive, Carrie Lam, has said her priority is to “stop the violence” rather than make political concessions, as the city’s two-month-long protest movement pressed on with a demonstration at the airport.

Lam said traffic disruptions and confrontations between police and protesters had hurt the economy, particularly the retail and food and beverage sectors. The demonstrations, however, are not abating and more are planned for this weekend, including at the airport, where protesters holding signs staged a sit-in at the arrival and departure halls on Friday.

Police said they had not received a formal application for the airport protest and warned against violence or disruptions that could endanger public safety. They have issued four objection letters for marches planned for the weekend.

Quick Guide What are the Hong Kong protests about? Show Why are people protesting? The protests were triggered by a controversial bill that would have allowed extraditions to mainland China, where the Communist party controls the courts, but have since evolved into a broader pro-democracy movement. Public anger – fuelled by the aggressive tactics used by the police against demonstrators – has collided with years of frustration over worsening inequality and the cost of living in one of the world's most expensive, densely populated cities. The protest movement was given fresh impetus on 21 July when gangs of men attacked protesters and commuters at a mass transit station – while authorities seemingly did little to intervene. Underlying the movement is a push for full democracy in the city, whose leader is chosen by a committee dominated by a pro-Beijing establishment rather than by direct elections.

Protesters have vowed to keep their movement going until their core demands are met, such as the resignation of the city’s leader, Carrie Lam, an independent inquiry into police tactics, an amnesty for those arrested and a permanent withdrawal of the bill. Lam announced on 4 September that she was withdrawing the bill. Why were people so angry about the extradition bill? Beijing’s influence over Hong Kong has grown in recent years, as activists have been jailed and pro-democracy lawmakers disqualified from running or holding office. Independent booksellers have disappeared from the city, before reappearing in mainland China facing charges. Under the terms of the agreement by which the former British colony was returned to Chinese control in 1997, the semi-autonomous region was meant to maintain a “high degree of autonomy” through an independent judiciary, a free press and an open market economy, a framework known as “one country, two systems”. The extradition bill was seen as an attempt to undermine this and to give Beijing the ability to try pro-democracy activists under the judicial system of the mainland. How have the authorities responded? Beijing has issued increasingly shrill condemnations but has left it to the city's semi-autonomous government to deal with the situation. Meanwhile police have violently clashed directly with protesters, repeatedly firing teargas and rubber bullets. Beijing has ramped up its accusations that foreign countries are “fanning the fire” of unrest in the city. China’s top diplomat Yang Jiechi has ordered the US to “immediately stop interfering in Hong Kong affairs in any form”. Lily Kuo and Verna Yu in Hong Kong

Signs held by protesters in the arrivals hall included ones saying “There are no rioters, only tyranny”, while pamphlets stacked in piles warned visitors of the heavy use of teargas by police. Officers said 800 canisters of the gas were used during protests on Monday alone, and journalists and protesters say many people suffered skin irritation and other injuries as a result.

Later on Friday, the UK foreign secretary, Dominic Raab, called for an independent investigation into the recent protests. In a phone call with Lam, Raab condemned the violence but emphasised the right to peaceful protest.

“The foreign secretary emphasised the need to find a way forward through meaningful political dialogue, and a fully independent investigation into recent events as a way to build trust,” the Foreign Office said in a statement.

“[He] condemned violent acts by all sides but emphasised the right to peaceful protest, noting that hundreds of thousands of Hong Kong people had chosen this route to express their views.”

“He underlined that the violence should not cloud the lawful actions of the majority.”

While the airport appeared to be operating normally, extra identification checks were in place for both travellers and employees, and airlines advised passengers to arrive earlier than usual for check-in.

However, China’s civil aviation authority issued a warning to Cathay Pacific about the involvement of its staff in “riots”. It said from this weekend, all personnel from the airline “involved in and supporting illegal demonstrations” would no longer be able to fly to mainland China or work there in air transportation. All Cathay Pacific crew members flying to the mainland will have to submit their identification details to Chinese authorities for approval before flights can proceed, it said.

During a general strike on Monday, more than 100 flights were cancelled because airline and airport employees were participating in the protest. Cathay Pacific was among the airlines most affected by the strike.

Hong Kong’s chief executive, Carrie Lam, at a press conference on Friday. Photograph: Jérôme Favre/EPA

There was no indication on Friday that police planned to use force to end what was planned as a three-day demonstration. A similar airport protest on 26 July ended peacefully.

At a briefing, police officer Vasco Williams said the force did not plan to issue an outright ban on demonstrations but would gauge each application based on the ability of organisers to maintain order.

“The police will closely monitor the situation this weekend and make respective deployment as necessary. It will be dependent on what happens at the time,” said Williams, the operations superintendent for the New Territories North district.

Williams and three other senior officers at the briefing repeatedly declined to answer questions about police tactics, including the alleged use of expired teargas, or the recall from retirement of the former deputy commissioner Lau Yip-shing.

Lau oversaw the response to pro-democracy protests five years ago in which police were accused of using excessive force. He began serving in the specially created temporary post of deputy commissioner of police for special duties on Friday.

The protests – which began two months ago over proposed extradition legislation under which suspects could have been sent to mainland China – have morphed into calls for broader democratic reforms in the semi-autonomous Chinese city, along with demands for the resignation of Lam and an independent investigation into alleged police abuse.

Lam said on Friday that an inquiry into police actions would not be appropriate while they were still responding to the demonstrations. Hongkongers have accused law enforcement of gross negligence after 44 civilians were attacked in a rail station last month by rod-wielding assailants apparently targeting protesters.

Police say 592 people have been arrested since 9 June, ranging in age from 13 to 76. They face charges including rioting, which carries a prison term of up to 10 years, along with interfering with police duties and taking part in unauthorised gatherings.

Demonstrators have at times wielded metal sticks, bricks, gasoline bombs and carts full of burning debris, and on several occasionsthey have been attacked by unknown people believed to be linked to organised crime groups.