The presidential party were reluctant to go through regular channels fearing public reactions, a security official said, and as a result, missed four flights that could have taken them to the United Arab Emirates.
Attempts to arrange a military flight to a neighbouring country also failed as clearance to land was not immediately available, the official added.
The president and his wife spent the night at a military airbase next to the airport.
A top defence source said the president’s closest military aides were discussing the possibility of taking him and his entourage overseas aboard a naval patrol craft.
“The best option now is to take the sea exit,” the defence official said. “He could go to the Maldives or India and get a flight to Dubai.”
The group left the airbase on Tuesday afternoon in two Bell 412 helicopters, an airport source said, bound for the northeastern port of Trincomalee, site of the naval base where Rajapaksa initially took refuge after fleeing his palace on Saturday.
Another option was to fly from Hingurakgoda air base where the choppers stopped to refuel, an air force source said, adding it had a runway that could accommodate executive jets.
Rajapaksa’s youngest brother Basil, who resigned in April as finance minister, missed his own Emirates flight to Dubai early Tuesday after a tense standoff with airport staff.
Basil – who holds US citizenship in addition to Sri Lankan nationality – tried to use a paid concierge service for business travellers, but airport and immigration staff said they had withdrawn from the fast track service.