A student leader threatened Wednesday to step up Hong Kong's huge pro-democracy protests -- including a possible occupation of government offices -- unless the city's leader steps down within a day, as support for the movement grew around the world.

The announcement came as tens of thousands of people poured onto the streets for a fourth straight night in protest against Beijing's refusal to grant full democracy to the semi-autonomous city, filling long stretches of major highways that normally teem with traffic.

Agnes Chow of the Scholarism student movement called on Hong Kong's embattled leader Leung Chun-ying to quit or face an escalation of the protests, which have sparked one of the biggest challenges to China's rule of the city since former colonial power Britain handed it back in 1997.

"If our Chief Executive and the central government (China) do not respect and listen to our people's opinion, we will consider having different operating actions in future days, including occupying other places like important government offices," said Chow, adding that the deadline was "today or tomorrow".

Wednesday marked China's National Day, with Leung clinking glasses of champagne at a reception with Chinese military and civilian officials as protesters booed outside.

Students have been at the forefront of the demonstrations in Hong Kong but others have swelled their ranks since riot police tear-gassed protesters on Sunday night in chaotic scenes that triggered an outpouring of support.

- We need to escalate the movement -

Chan Kin-man, co-founder of the pro-democracy Occupy Central group which co-organised the demonstrations, said any escalation would be "an action initiative by the students" and called for it to be peaceful.

There was a mixed response to the proposal from the protesters packed into the streets on Wednesday night despite the sweltering heat, spraying their faces with water to keep cool.

"We need to escalate the movement," said 23-year-old student Jason Chan. "So many people have come out every day and the government hasn't responded to us. If we don't take things to the next level, this movement is pointless."

But many others were reluctant to take any action that could prompt further clashes with the police. Sunday night's violence has given way to peaceful mass demonstrations, with a carnival atmosphere prevailing after police retreated.

"I think we should keep this a peaceful revolution and shouldn't be more intense," said costume designer Janice Pang as she helped collect plastic bottles in the protest zone to be recycled.

"Hong Kong people may not support us if we do something more extreme."

The protesters are furious at the central government's refusal to allow free elections for the city's next leader in 2017, insisting that only two or three candidates vetted by a pro-Beijing committee will be permitted to stand.

They call this "fake democracy" and have two demands -- that Leung steps down and that Beijing reverses its decision.

"Hong Kong and the mainland are closely linked in their development," Leung told attending dignitaries on Wednesday.

"We must work hand in hand to make the Chinese dream come true."

In a movement being dubbed the 'umbrella revolution' -- a nod to the umbrellas they have used to protect themselves against tear gas, the sun and torrential downpours alike -- the protesters have brought key parts of the city to a standstill, heavily disrupting the transport network and shutting down businesses.

Wednesday and Thursday are both public holidays in Hong Kong, leaving many workers free to swell the masses in the streets.

- Supporters around the globe -

Huge crowds cheered on Wednesday night as messages of support from around the world were projected onto the city's main government building -- including words of encouragement from supporters in mainland China.

Support for the protesters has been growing worldwide, with a Facebook group calling itself "United for Democracy: Global Solidarity with Hong Kong" planning events from Australia to the United States.

More than 1,000 sympathisers gathered in the Taiwanese capital Wednesday night, while 80 attended a candlelight vigil in Singapore.

About 15 demonstrators, bearing umbrellas, gathered outside the Chinese embassy in Washington DC, which was closed for a holiday.

"We have to do everything to head off a Tiananmen in Hong Kong," said organiser Yang Jianli of the Initiatives for China NGO, referring to the crackdown on student-led protests in Beijing in 1989 during which hundreds -- by some estimates, more than a thousand -- people died.

But Hong Kong's protests pose a huge political challenge for Beijing at a time when the Communist Party is cracking down hard on dissent on the mainland.

In comments to mark National Day, Chinese President Xi Jinping said "all tumours grown on the healthy organism" of the Communist Party must be removed.

"We must never waver in our faith and must never separate ourselves from the people," Xi added at a ceremony Tuesday.

Rights groups say Chinese authorities have detained more than a dozen activists and questioned as many as 60 others who expressed support for the Hong Kong crowds.

The Wall Street Journal reported that Leung's administration is planning to sit out the protests -- hoping they fizzle out rather than trying to clear them by force -- on Beijing's orders.

"Beijing has set a line to C.Y. (Leung). You cannot open fire," the newspaper quoted a source familiar with the matter as saying. "You must halt it in a peaceful way."