Hong Kong's Chief Executive CY Leung says he will not resign, but has offered talks between his government and pro-democracy protesters.
The leaders of mass demonstrations have welcomed proposed talks, but still insist that Mr Leung should step down.
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 Hong Kong government buildings, but have been warned not to try and occupy them.
At a news conference shortly before the protesters' midnight deadline for his resignation, the chief executive said attempting to occupy building would lead to "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," Mr 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."
He added: "I will not resign because I have to continue with the work for elections."
Student protest leaders responded by saying that they planned to join the talks with the government but insisted that Mr Leung should step down, saying he had "lost his integrity".
A wider pro-democracy group that has joined the demonstrations, Occupy Central, issued a statement saying it "hopes the talks can provide a turning point in the current political stalemate".
It added: "However, we reiterate our view that Chief Executive Leung Chun-ying is the one responsible for the stalemate, and that he must step down."
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