Hong Kong pro-democracy protesters demanded that the city's embattled leader meet a deadline to resign on Thursday, as China warned the United States against meddling in its "internal affairs".

Demonstrators, who have shut down central areas of the southern Chinese city for four days, have given chief executive Leung Chun-ying until midnight to step down, or face escalated action.

In Washington, Beijing warned the United States to back off, in its strongest riposte yet to worldwide supporters of the suffrage movement sweeping the southern Chinese city.

"Hong Kong affairs are China's internal affairs," Foreign Minister Wang Yi told US Secretary of State John Kerry at a press conference.

"All countries should respect China's sovereignty and this is a basic principle of governing international relations," Wang said sternly.

He added that Beijing would not tolerate "illegal acts that violate public order".

Kerry replied urging Hong Kong authorities to "exercise restraint and respect the protesters' right to express their views peacefully."

Four days of peaceful demonstrations have seen tens of thousands of people take over usually traffic-heavy streets in Hong Kong as they demand Beijing grant free elections in the semi-autonomous city.

The demonstrators consider Leung a Beijing stooge and protest leaders want Thursday's ultimatum to be met.

"We will consider having different operating actions in future days, including occupying other places like important government offices," said Agnes Chow of student movement Scholarism.

Protester Thomas Choi told AFP: "We want to talk to him face to face."

'We need to escalate'

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

With Wednesday and Thursday both public holidays in Hong Kong, many workers have been free to swell the masses in the streets.

Vast crowds poured in for a fourth sweltering night Wednesday.

"We need to escalate the movement," said 23-year-old student Jason Chan. "If we don't take things to the next level, this movement is pointless."

But others were reluctant to take any action that could prompt further clashes with the police.

"I think we should keep this a peaceful revolution," said costume designer Janice Pang.

"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 as well as demanding Leung step down, they also want Beijing to reverse its decision.

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.

Worldwide support grows

China's call came as support for the protesters has been growing worldwide, with thousands rallying Wednesday to back the protests.

About 4,000 people turned out in Taipei while in London 2,000 people gathered outside the Chinese embassy.

Crowds in Hong Kong cheered late Wednesday as messages of support from around the world were projected onto the main government building -- including from sympathisers in mainland China.

Chris Patten, the last British governor of Hong Kong, told BBC radio the entire situation had been "very, very badly mishandled", calling on authorities to enter into consultation with demonstrators.

"I think we've got to see dialogue replacing tear gas and pepper spray," he said, adding that China was reneging on its promises to allow the city to manage its own affairs.

The protests pose a huge political challenge for Beijing at a time when the Communist Party is cracking down hard on dissent on the mainland.

Authorities have scrubbed mentions of the protests from Chinese social media, while rights groups say more than a dozen activists have been detained and as many as 60 others questioned for expressing support for the Hong Kong crowds.

In a sign of Beijing's growing unease, a local tourism leader said Chinese travel agents were reporting that group visits to the city had been suspended.

October 1-7 is known as "Golden Week" in mainland China, a key shopping holiday that sees many travel to Hong Kong.