Hong Kong’s leader Carrie Lam has insisted she never offered to resign, after an audio recording was leaked in which she appeared to suggest she would quit as chief executive if she could.

Weeks after reports that China has “repeatedly refused” the chief executive’s offers to tender her resignation, Reuters released a recording on Monday in which Ms Lam could be heard saying: “If I have a choice, the first thing is to quit.”

Speaking at a news conference on Tuesday, Ms Lam did not deny the authenticity of the recording, although she said it was “totally unacceptable” that comments from a private meeting with business leaders had been leaked.

She instead suggested the comments were being taken out of context, and that in the business leaders’ meeting she was trying to explain her thought process for staying on as leader.

Hong Kong has entered its 14th consecutive week of protests, with thousands of students and some school pupils again boycotting classes on Tuesday despite the end of the summer holidays.

What started out as a series of demonstrations against an unpopular extradition bill has expanded into a broad-based protest movement seeking to defend Hong Kong’s democratic freedoms from perceived encroachment by Beijing.

In the audio recording, Ms Lam could be heard saying she felt it was unforgivable for a chief executive to have presided over such a crisis. She suggests the weeks of unrest were her fault for introducing the now-suspended bill, and that her preferred course of action would have been “having made a deep apology… to step down”.

During the chief executive’s weekly media briefing on Tuesday, she was asked repeatedly why Beijing would not let her step aside – one of the key demands of the protest movement.

But Ms Lam said that “not resigning was my own choice… I have not given myself the choice to take an easier path and that is to leave”.

“I have never tendered a resignation to the central people’s government. I have not even contemplated to discuss a resignation,” she said.

Ms Lam was selected to be leader in 2017 from a shortlist of pro-Beijing candidates, in a vote by Hong Kong elites. Protest leaders in the city are now demanding that the process of electing a chief executive be opened up – something the Chinese government said in 2014 it would not allow.

Protesters at Hong Kong University on Tuesday criticised Ms Lam for failing to listen to any of what they call their “five demands”.

Aside from the matter of the chief executive’s position, they are for the complete withdrawal of the extradition bill, an amnesty for all arrested demonstrators, for police to stop categorising rallies as “riots” and for an independent inquiry into allegations of police violence.

Continuing protests rock Hong Kong: In pictures Show all 35 1 /35 Continuing protests rock Hong Kong: In pictures Continuing protests rock Hong Kong: In pictures Police officers point their guns towards pro-democracy protesters after a clash at a march in Hong Kong on August 25 Reuters Continuing protests rock Hong Kong: In pictures Pro-democracy protesters throw molotov cocktails during clashes with riot police in Hong Kong on August 25 Reuters Continuing protests rock Hong Kong: In pictures Demonstrators rally behind barricades ass they are shrouded in tear gas deployed by police in Hong Kong on August 25 Reuters Continuing protests rock Hong Kong: In pictures Police clash withpro-democracy protesters at a march in Hong Kong on August 25 Reuters Continuing protests rock Hong Kong: In pictures A police officer prepares to strike a protester as clashes erupt during a pro-democracy march in Hong Kong on August 24 AFP/Getty Continuing protests rock Hong Kong: In pictures A water cannon is fired by riot police to clear the street of demonstrators during a protest in Hong Kong on August 25 EPA Continuing protests rock Hong Kong: In pictures Pro-democracy protesters use a slingshot during clashes with riot police in Hong Kong on August 25 Reuters Continuing protests rock Hong Kong: In pictures Riot police fire tear gas to disperse pro-democracy protesters in Hong Kong on August 24 Reuters Continuing protests rock Hong Kong: In pictures A demonstrator throws a molotov cocktail as they clash with riot police during a protest in Hong Kong on August 25 Reuters Continuing protests rock Hong Kong: In pictures A demonstrator swings a tennis racket in an attempt to knock back a tear gas cannister thrown by riot police during a protest in Hong Kong on August 25 Reuters Continuing protests rock Hong Kong: In pictures A protester displays a Hong Kong Independence flag during a pro-democracy march in Hong Kong on August 24 EPA Continuing protests rock Hong Kong: In pictures Riot police tend to a detained demonstrator who has been injured during a protest in Hong Kong on August 25 Reuters Continuing protests rock Hong Kong: In pictures A demonstrator uses bamboo poles to build a barricade during a protest in Hong Kong on August 25 Reuters Continuing protests rock Hong Kong: In pictures Riot police clash with demonstrators during a protest in Hong Kong on August 24 Reuters Continuing protests rock Hong Kong: In pictures Protesters are hit by tear gas fired by the police in Hong Kong on August 24 AFP/Getty Continuing protests rock Hong Kong: In pictures Demonstrators shrouded in tear gas shield themselves behind barricades during a clash with riot police in Hong Kong on August 25 Getty Continuing protests rock Hong Kong: In pictures Riot police arrest a protester during a pro-democracy march in Hong Kong on August 24 EPA Continuing protests rock Hong Kong: In pictures Police clash with pro-democracy protesters at the Hong Kong international airport on August 13 AFP/Getty Continuing protests rock Hong Kong: In pictures Protesters fall back as they clash with police during a protest at Kowloon Bay in Hong Kong on August 24 AFP/Getty Continuing protests rock Hong Kong: In pictures Police clash with pro-democracy protesters at the Hong Kong international airport on August 13 Reuters Continuing protests rock Hong Kong: In pictures Riot police move to disperse protesters during a clash at the Hong Kong international airport on August 13 Reuters Continuing protests rock Hong Kong: In pictures Commuters riding in a bus drive past protesters in Hong Kong's Kowloon Bay on August 24 AFP/Getty Continuing protests rock Hong Kong: In pictures Protester hold umbrellas as they take part in a pro-democracy march in Hong Kong on August 24 EPA Continuing protests rock Hong Kong: In pictures Riot police detain a demonstrator as they clash during a protest in Hong Kong on August 24 Reuters Continuing protests rock Hong Kong: In pictures Pro-democracy protesters block the entrance to the airport terminals after clashes with police at the Hong Kong international airport on August 13 AFP/Getty Continuing protests rock Hong Kong: In pictures Riot police spray pepper spray as shield themselves by a police van during a clash with pro-democracy protesters at the Hong Kong international airport on August 13 Reuters Continuing protests rock Hong Kong: In pictures Riot police use pepper spray to disperse protesters during a demonstration at the Hong Kong international airport on August 13 Reuters Continuing protests rock Hong Kong: In pictures Demonstrators shrouded in tear gas shield themselves behind barricades during a clash with riot police in Hong Kong on August 25 Reuters Continuing protests rock Hong Kong: In pictures Medical professionals gather to protest police brutality at the Queen Elizabeth Hospital in Hong Kong on August 13 Getty Images Continuing protests rock Hong Kong: In pictures Police detain a pro-democracy protester at the Hong Kong international airport on August 13 AFP/Getty Continuing protests rock Hong Kong: In pictures A protester is halted by police during an occupation at the Hong Kong international airport on August 13 AP Continuing protests rock Hong Kong: In pictures Police clash with pro-democracy protesters at the Hong Kong international airport on August 13 AFP/Getty Continuing protests rock Hong Kong: In pictures Police stand guard at the entrance of the departure terminals at the Hong Kong international airport on August 13 AFP/Getty Continuing protests rock Hong Kong: In pictures Protesters continue their occupation at the Hong Kong international airport on August 14 AP Continuing protests rock Hong Kong: In pictures Travellers read placards and posters left by pro-democracy protesters at the Hong Kong international airport on August 14 AP

“I think Carrie Lam doesn’t have much power,” Poon, a 21-year-old engineering student said. “Whether she can step down or not, it doesn’t matter. Chief executive is still chosen by the central government. What matters is if she refuses to respond to the five demands. She’s an irresponsible leader.”

The school and university boycotts follow on from one of the worst weekends of violent clashes in Hong Kong in recent weeks.

After the police attempted to ban a planned march on Saturday, protesters set up and burned barricades, and threw petrol bombs. On Sunday, thousands gathered to block key roads and public transport links to Hong Kong airport, and smashed turnstiles and other public property at an MTR station. Police retaliated on both days with water cannons, tear gas and baton charges.

More than 1,100 people have been detained since the unrest began, including prominent activists like the 2014 Umbrella Movement leader Joshua Wong.

Mr Wong was held and then bailed on Friday in what his party, Demosisto, called an attempt to intimidate the protest movement.

On Tuesday, he spoke at an event in Taipei, calling on the Taiwanese people to hold their own demonstrations as they face their own pressures from China.

“A lot of people in the past have said ‘today Hong Kong and tomorrow Taiwan’,” Mr Wong said, a reference to China’s suggestion that Taiwan could be ruled by Beijing under the same “one country, two systems” principle that it applies to Hong Kong.