Hong Kong demonstrators have rejected demands immediately to end rallies that have paralysed the city’s downtown, their numbers swelling for a third night.

Protest leaders are confident of mustering massive crowds, angered at Beijing’s refusal to grant full democracy, overnight and into Wednesday for the National Day public holiday marking the 65th anniversary of the founding of Communist China.

• Aerial footage shows massive scale of Hong Kong protests
• The protest that shut down Hong Kong’s CBD

Thousands ignored a call from the city’s embattled leader to end the sit-in, as well as Beijing’s branding of their demonstrations as “illegal”, to take to the streets of the key financial hub.

A heavy downpour briefly sent umbrellas skyward and crowds scurrying, but the prospect of bad weather left the crowds undeterred.

“We have spent more than a week under the sun, under pepper spray, we of course can stand the rain. Nothing can stop us,” a recent university student who identified himself as Choi told AFP.

Beijing has been left grappling with one of the biggest challenges to its rule over the semi-autonomous city at a time when the Communist Party is cracking down hard on dissent on the mainland.

In his first public comments since demonstrators were tear-gassed by riot police on Sunday evening, Chief Executive Leung Chun-ying said the pro-democracy sit-in organised partly by the Occupy Central group was now “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,” he said.

But protest leaders rejected Leung’s demands and renewed calls for the Beijing-backed leader to step down.

The demonstrations, the most intense civil unrest Hong Kong has experienced since its 1997 handover from British rule, were sparked by Beijing’s decision in August to restrict who can stand for the city’s top post.

British Deputy Prime Minister Nick Clegg said on Tuesday he will summon China’s ambassador to London over the protests to express his “dismay and alarm” about the refusal to grant free elections.

Hong Kongers will be able to vote for their next chief executive in 2017 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.