Hong Kong leader Carrie Lam has denied ever offering to resign, after audio was leaked of her saying she would if she could.
On Monday, a recording of a private meeting emerged where she is heard saying: "If I have a choice, the first thing is to quit."
She said on Tuesday she had "never tendered any resignation", but did not deny the authenticity of the recording.
Hong Kong has seen months of anti-government protests.
The protests were sparked by changes to a law that would allow extradition to mainland China, but have since widened to include calls for an independent inquiry into police brutality and demands for greater democracy.
Ms Lam, who introduced the now-shelved bill, has been the target of much of the protesters' anger.
What's in the leaked audio?
The audio, published by Reuters on Monday, was recorded at a private meeting of business leaders that Ms Lam attended last week.
In it she is heard blaming herself for igniting the territory's political crisis, saying it was unforgiveable of her to have caused such huge havoc.
"If I have a choice, the first thing is to quit, having made a deep apology, is to step down," the voice on the tape says.
She says she has little power to handle the city's current crisis, explaining she has to serve both Beijing and Hong Kong.
"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 manoeuvring is very, very, very limited," she says on the tape.
She also says in the recording that China does not have a deadline by which it wants to solve the crisis in Hong Kong, and that Chinese authorities would not send in troops to end the protests.