On Wednesday, Rosa, an airport official who would not give her surname, told Reuters: "All flights since last night [Tuesday] have been cancelled until today. The reason for this is because there will be no security guarantee for the passengers."
The closure came amid violent clashes among youth gangs armed with guns, bows and arrows and rocks near the airport. Police and local residents said that twelve houses were burned in the fighting.
The first clash happened late on Tuesday on a main road leading to the airport with one person killed by gunfire. Another clash broke out early on Wednesday, killing another resident.
Security forces had closed the road.
Nelson, who lives near the area and did not give his surname, said: "There were provocateurs in the road that leads to the airport. They burned tyres and blocked the road."
An Australian police officer said many shots were fired during the clashes.
Battles among gangs of youths are common in the impoverished country, which gained full independence from Indonesia in 2002.
The former Portuguese colony plunged into chaos four months ago when a series of protests developed into widespread violence after 600 members of the 1,400-strong army were sacked.
An estimated 100,000 people were displaced in the fighting, which led to the deployment of a 2,500-strong international peacekeeping force.
A strengthened police element in the force has so far struggled to contain sporadic violence.
Concerns about East Timor's fragile security grew after a rebel leader, Major Alfredo Reinado, escaped from jail in Dili last month with 50 other inmates.
Reinado, a key player behind the revolt in May, has called for a "people power" revolution in a letter circulating in the country.