The protests on Monday were driven by anger over alleged police brutality, with demonstrators claiming one woman had lost an eye at a weekend rally and video showing tear gas being used against them in a subway station.
But the protests have led to rising anger from authorities in Beijing, who on Monday described some of the violent demonstrations as "terrorism".
State-run media on Monday also showed armoured personnel carriers assembling at a mainland city just across the border from Hong Kong.
Early Tuesday, passengers with luggage were being checked in at the departures hall and information boards showed several flights were boarding or about to depart.
But the woes at the airport remained far from over, with a massive backlog of flights to clear and activists calling for another protest there on Tuesday afternoon.
Cathay Pacific, Hong Kong's flagship airline, listed more than 200 flights as still being cancelled on Tuesday morning.
It an advisory posted on its website at 6:00 am (2200 GMT Monday), Cathay said passengers urged customers to postpone non-essential travel from Hong Kong.
On Tuesday morning, only a handful of protesters remained in the airport. But fears of a police operation to clear the facility overnight proved unfounded, with demonstrators simply leaving by themselves.
Many of the posters and artwork they had hung throughout the facility during the hours-long rally had been taken down, but graffiti -- some reading "an eye for an eye" -- could still be seen in several places.
The protesters adopted the slogan after a woman suffered a serious facial injury that reportedly caused her to lose the vision in one eye at a demonstration that turned violent on Sunday night.
The demonstrators accuse police of causing the injury by firing a bean-bag round and cite the case as evidence of what they say has been an excessive and disproportionate response by police to their protests.
The activists have called on their supporters to return to the airport later on Tuesday, though it was unclear whether authorities would allow that to happen.
The protests that began in opposition to a bill allowing extradition to the mainland has morphed into a broader bid to reverse a slide of freedoms in the southern Chinese city.
But the city's Beijing-backed leader has ruled out meeting the protesters' demands, which include the right to choose their next leader and an investigation into alleged police brutality.
The demonstrations have become increasingly violent, with police using tear gas and rubber bullets to push back protesters who have sometimes hurled bricks and bottles.
"It is becoming more and more dangerous, but if we don't still come out at this point, our future will become more frightening, and we will lose our freedoms," a 22-year-old protester at the airport told AFP on Monday.
China warns of 'terrorism'
The movement has infuriated Beijing, where authorities Monday slammed violent protesters who threw petrol bombs at police officers, linking them to "terrorism".
"Hong Kong's radical demonstrators have repeatedly used extremely dangerous tools to attack police officers, which already constitutes a serious violent crime, and also shows the first signs of terrorism emerging," said Yang Guang, spokesman for the Hong Kong and Macao Affairs Office of the State Council.
"This wantonly tramples on Hong Kong's rule of law and social order."
Hours later, two state media outlets ran videos showing armoured personnel and troop carriers purportedly driving to Shenzhen, which borders Hong Kong.
And a commentary early Tuesday on China's official Xinhua news agency spoke of "black-clad mobsters" and said Hong Kong's future is at a "critical juncture".
A senior official in the administration of US President Donald Trump on Monday urged "all sides" to avoid violence in Hong Kong.
"Societies are best served when diverse political views are respected and can be freely and peacefully expressed," the official said on condition of anonymity.
The abrupt shutdown of one of the world's busiest hubs came after thousands of black-clad demonstrators flooded the airport for a peaceful rally.