Hong Kong's chief executive, Carrie Lam, said she would quit if she had a choice, according to newly released audio obtained by Reuters.

She added that her government had "very limited" capacity to restore peace to the territory because China saw the unrest as a threat to its national security and authority.

"The political room for the chief executive who, unfortunately, has to serve two masters by constitution, that is the Central People's Government and the people of Hong Kong, that political room for maneuvering is very, very, very limited," she said in the tapes.

Lam at a press briefing on Tuesday local time did not deny that she made the remarks documented in the leaked audio but said she "never tendered" her resignation to China and repeated that she would not be stepping down in the face of intensifying protests entering their 13th week.

Hong Kong's leader, Carrie Lam, told a group of business leaders in the city that she would quit if she had a choice, according to leaked audio of her remarks obtained by Reuters, amid increasing calls from protesters for her to resign.

Protests in Hong Kong have entered their 13th week and show no sign of slowing. What began as protests against a bill that would have allowed extraditions to the Chinese mainland have ballooned into a fight to uphold democracy in the city, and protesters have called for Lam's resignation, alongside other central demands.

According to Reuters, Lam made the comments at a closed-door meeting last week and said she had wreaked "unforgivable havoc" on the semiautonomous Chinese territory by putting forth the bill.

"If I have a choice," she said in English as she fought back tears, "the first thing is to quit, having made a deep apology.

"So I make a plea to you for your forgiveness."

She added that she had "very limited" capacity to restore peace to the territory because the issue had escalated into a national security situation for China that was beyond the capacity of her local government's abilities.

"The political room for the chief executive who, unfortunately, has to serve two masters by constitution, that is the Central People's Government and the people of Hong Kong, that political room for maneuvering is very, very, very limited," she said in the tapes.

Lam says China has 'absolutely no intention' of military intervention in Hong Kong

She also reassured those in the meeting that China had "absolutely no intention" of deploying its People's Liberation Army, which in recent weeks has increased its presence along the Hong Kong border in the Chinese city of Shenzhen. She added that "Beijing did not have a deadline" for ending the protests in Hong Kong.

Military vehicles gathered in the soccer stadium at the Shenzhen Bay Sports Center. Associated Press

"It would be naive of me to paint you a rosy picture that things will be fine or [that] I have a deadline," she said, adding that the city would be celebrating China National Day on October 1, which commemorates the founding of the People's Republic of China, but with "modest" and "solemn" modifications as not to further inflame tensions.

Dozens of military vehicles entered Hong Kong last week for what state media called a "routine rotation" of its officers stationed in Hong Kong.

But while China has signaled it is ready to use force if necessary, experts remain skeptical that Chinese military intervention in Hong Kong is imminent and say recent displays are part of a wider strategy aimed at intimidation and deterrence.

Read more: China appears to be gearing up for a military intervention in Hong Kong, but experts say Beijing is most likely bluffing

China also reportedly struck down a plan by Lam to withdraw the extradition bill

Lam's statements appear to confirm a report by Reuters last week that said China blocked efforts by Hong Kong's government to withdraw the extradition bill from being debated. Lam announced that the bill was "dead" in July, but it has not been struck in its entirety.

A demonstrator throwing back a tear-gas canister during a clash with the riot police in Hong Kong on August 24. Tyrone Siu/Reuters

According to Reuters, citing testimony from Chinese and Hong Kong government officials, Lam suggested that giving in to at least one protester demand would ease demonstrations, though the Chinese government refused to budge on its position.

On Sunday, Chinese state media warned that the "end is coming for those attempting to disrupt Hong Kong and antagonize China." It did not specify how it planned to end protests but said any threats to China's national sovereignty and security remained a bottom line for the country that "must not be crossed."

Protesters over the weekend clashed with the police and blocked roads and disrupted train services leading to Hong Kong International Airport, forcing travelers to walk.

Lam at a press briefing on Tuesday local time did not deny that she made the remarks documented in the leaked tapes but said she "never tendered any resignation" to China and repeated that she would not be stepping down in the face of intensifying protests.

"I know it's not going to be an easy path," she said. "I'd rather stay on and walk this path, together with my team, and with the people of Hong Kong."

A recent independent survey found that Lam's approval rating had sunk to 24.6% in recent months and that popular trust in the Hong Kong government was at an all-time low.