CY Leung said his government was willing to hold talks with the protesters.
The protesters are angry at China’s plan to vet candidates for elections in 2017, and say they want full democracy.
They have surrounded two key government buildings in the territory, but CY Leung warned them that they were breaking the law.
At a news conference shortly before the protesters’ midnight deadline for his resignation, CY Leung warned that attempts to move on or occupy government buildings would have “very serious consequences”.
He said the territory’s top civil servant, Chief Secretary Carrie Lam, would open a dialogue with student leaders as soon as possible.
“Tonight, the Hong Kong Federation of Students issued an open letter asking for a meeting with the chief secretary, representing the Hong Kong government, to discuss one item – and this is the constitutional development of Hong Kong,” CY Leung told reporters.
“We have studied the letter in detail, and I’m now appointing the chief secretary to represent the Hong Kong government to meet with the representatives of the Hong Kong Federation of Students to discuss constitutional development matters.”
Hong Kong’s chief executive added: “I will not resign because I have to continue with the work for elections.”
The protesters have massed outside the Office of the Chief Executive and the Central Government Complex.
Police had earlier warned protesters not to try to breach the police cordon protecting the buildings.
Police spokesman Steve Hui told reporters: “The police will not stand by and watch. We will decisively uphold the law.”
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