Chinese President Xi Jinping, who has taken a hard line against any perceived threat to the Communist Party's hold on power, meanwhile vowed in a National Day speech to "steadfastly safeguard" Hong Kong's prosperity and stability.
He said Beijing believes Hong Kong will "create an even better future in the big family of the motherland."
China's government has condemned the student-led protests as illegal, though so far it has not overtly intervened, leaving Hong Kong's semi-autonomous government to handle the crisis.
Leung's statement drew a defiant response from the students.
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"If Leung Chun-ying doesn't come out to Civic Square before midnight ... Then I believe inevitably more people will come out onto the streets," said Alex Chow, secretary general of the Hong Kong Federation of Students, the organiser of the university class boycotts that led to the street protests.
Chow said the students were considering various options, including widening the protests, pushing for a labor strike and possibly occupying a government building.
Both sides appeared to be waiting out the standoff, as police continued the light-handed approach to the protests they adopted after their use of tear gas and pepper spray over the weekend failed to drive out tens of thousands of people occupying streets near the government headquarters.
The sit-ins instead spread to the financial district and other areas.
A brief cloudburst today cooled the air, seeming to energise the protesters, a group of whom shouted "Jiayou," or "Keep it up," and waved their cellphones with bright LED flashlights sparkling in the dark.