Protesters rallied and unfurled banners late into the night in the Wong Tai Sin area of Hong Kong's Kowloon district

Hong Kong may curb access to the internet in a bid to contain months of increasingly violent pro-democracy protests, a cabinet member told AFP on Monday, after an emergency-law ban on demonstrators wearing face masks failed to quell the unrest.

The warning came as the international financial hub remained partly paralysed from three days of protests in which the city's rail network and business outlets seen as pro-China were badly vandalised.

The surge in protests was in response to the Hong Kong government's announcement on Friday it would invoke colonial-era emergency laws not used for more than 50 years to ban demonstrators from wearing face masks.

Chief Executive Carrie Lam said the ban was needed to contain the unrest, which began nearly four months ago and has seen millions of people take to the streets demanding China stop strangling their freedoms.

Ip Kwok-him, a veteran pro-Beijing politician and member of Hong Kong's executive council, fuelled those concerns when he said controls on the internet could be introduced.

"The government will not rule out the possibility of placing a ban on the internet," he told AFP.

Ip said the internet has been crucial to protesters, who have no public leaders and use online forums and encrypted messaging apps to mobilise.

But he said the government recognised any online shutdown could have a knock-on effect.

"I think a condition for implementing the internet ban would be not to affect any businesses in Hong Kong," he said.

The executive council is Hong Kong's cabinet, an advisory body to Lam.

She announced the ban on face masks immediately after meeting with the council on Friday.

Asked about the protests, US President Donald Trump said that Washington wants to see a "humane solution" to the crisis -- even as he noted that the crowds of protesters were getting smaller.

"I would just like to see a humane deal worked out and I think [Chinese] President Xi [Jinping] has the ability to do it" Trump said.

"Maybe they can work out something amicable."

Trump also marveled at the pro-US sentiment among the protesters. "They have tremendous signage and a tremendous spirit for our country. A lot of American flags. A lot of Trump signs," he said.

- More clashes, mask arrests in court -

On Monday night, hardcore protesters returned to the streets, vandalising store fronts, blocking roads in multiple areas and trashing two subway stations.

Police fired tear gas in at least three locations, although the clashes were less sustained and widespread than in recent nights.

A group of protesters however vandalized a Bank of China branch in the Tseung Kwan O neighbourhood of Kowloon, destroying property and spray-painting slogans on the walls.

Earlier in the day, a male university student and a 38-year-old woman were the first people to be charged with illegally wearing masks as supporters packed the courtroom -- many wearing face coverings.

They were charged with unlawful assembly, which carries up to three years jail time, and with defying the mask ban, which has a maximum one-year sentence. Both were released on bail.

Outside the court, demonstrators queued to get in, some chanting slogans such as "Wearing a face mask isn't a crime" and "The law is unjust".

Many said they feared the mask ban was just the first of more emergency orders to come.

"It's an excuse to just introduce other totalitarian laws, next is martial law," one protester outside the court, who gave his surname Lo, told AFP.

- Few concessions -

The protests were ignited by a now-scrapped plan to allow extraditions of criminal suspects to the mainland.

This fuelled fears of an erosion of liberties promised under the 50-year "one country, two systems" model China agreed to ahead of the 1997 handover by Britain.

After Beijing and local leaders took a hard stance against the initial protests, they snowballed into a movement calling for more democratic freedoms and police accountability.

The past week has seen a particularly intense stretch of protests.

The worst clashes to date erupted last Tuesday as China celebrated 70 years of Communist Party rule, with a teenager shot and wounded by police as he attacked an officer.

Large parts of the railway network -- which carries millions of passengers daily -- closed over the weekend because of vandalism, while many shops and malls were shuttered.

Some subways stations and shops remained closed on Monday, a public holiday in Hong Kong.

On the mainland, Beijing flexed its muscles by pulling a top US basketball team's games from state broadcaster CCTV after its manager posted a tweet featuring the message "Fight for Freedom. Stand with Hong Kong".

The Houston Rockets tried to calm the waters, later issuing apologies from players and the manager.