Speaking early on the National Day holiday, CY Leung said Hong Kong should work with Beijing to achieve progress.
The protesters want Beijing to withdraw plans to vet candidates for the next Hong Kong leadership election in 2017.
Activists say they expect the biggest demonstrations yet on the streets to coincide with the holiday.
By midday, protesters were starting to fill up the main protests site in the Central business district, Causeway Bay and Mong Kok. A fourth protest site has also spread to Canton Road in Tsim Sha Tsui, several roads south of Mong Kok.
CY Leung, Hong Kong’s chief executive, has rejected campaigners’ calls for him to stand down. Chinese President Xi Jinping has reaffirmed Beijing’s control over the territory.
A rumbling protest campaign ballooned into mass street demonstrations at the weekend.
Police responded initially with tear gas and pepper spray, but riot police later withdrew and since early on Monday the situation has remained calm.
Crowds swelled again on Tuesday night and the demonstrators – who include student groups, supporters of the Occupy Central movement and others angered by the police response – say they are confident of greater numbers on Wednesday, October 1.
So far there are no signs of concessions from Beijing.
On September 30, President Xi Jinping told Communist Party leaders that his government would “steadfastly safeguard the long-term prosperity and stability of Hong Kong and Macau”.
The protests are seen as a direct challenge to Beijing’s grip on the territory’s politics. Analysts say leaders are worried that calls for democracy could spread to mainland cities.
News of the protests is being heavily censored in mainland China. Media have blamed “radical opposition forces” for stirring up trouble.
Meanwhile the US restated its position on the protests, saying that a genuine choice of candidates in the election would enhance the legitimacy of the chief executive.
On September 30, state department spokeswoman Jen Psaki said that Secretary of State John Kerry would discuss the protests with Chinese Foreign Minister Wang Yi when the pair meet on October 1.
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