In his first public comments since demonstrators were tear gassed by riot police on Sunday evening, chief executive Leung Chun-ying said protests organised by the pro-democracy Occupy Central group had got "out of control".
"Occupy Central founders had said repeatedly that if the movement is getting out of control, they would call for it to stop. I'm now asking them to fulfil the promise they made to society, and stop this campaign immediately," Leung said.
But protest leaders immediately rejected Leung's demands and renewed their calls for him to step down.
"If Leung Chun-ying announces his resignation, this occupation will be at least temporarily stopped in a short period of time, and we will decide on the next move," co-founder Chan Kin-man told reporters after Leung's comments.
The protests have left Beijing grappling with one of the biggest challenges to its rule of the semi-autonomous city at a time when the Communist Party is cracking down hard on dissent on the mainland.
The demonstrations, the worst civil unrest Hong Kong has experienced since its 1997 handover from British rule, were sparked by Beijing's decision last month to restrict who can stand for the city's top post.
Hong Kongers will be able to vote for their next chief executive in 2017 elections but only two or three candidates vetted by a pro-Beijing committee will be allowed to stand -- something demonstrators have labelled a "fake democracy" that shows Hong Kong cannot trust its mainland overseers.
But Leung said Beijing would never be persuaded to change its stance by the protesters while they occupy streets.
"The central government will not be coerced into submission because some people have used illegal actions," he said.
Schools in affected areas Tuesday were again closed and commuters faced disruption, with many bus routes suspended or rerouted and taxis scarce.
Throughout the morning protester numbers dwindled from their overnight highs, when tens of thousands turned the city's downtown into a carnival after riot police withdrew.
But those manning the barricades showed no signs of backing down, digging in for a third day of occupying major thoroughfares.