The assaults, which took place Saturday evening and Sunday morning in the immediate wake of the inauguration of Ukraine's new President Petro Poroshenko, did not result in any injuries among the defenders, he said.
"It was clear the rebels were trying to destroy the building which controls the power supply to the airport," said the source, one of the Ukrainian paratroopers guarding the airport, talking to AFP by telephone.
"It's the first time we have had an attack of this kind. Up till now, we've only had a few skirmishes," said the soldier, who identified himself only as Sergiy.
Pro-Russian separatist proclaimed the independence of the "Lugansk People's Republic" in May, at about the same time as the neighbouring "Donetsk People's Republic".
The two districts have been the scene of ceaseless fighting between Ukrainian forces and pro-Russian insurgents that have killed more than 200 people since mid-April.
When approached by AFP, a spokesman for the "Lugansk People's Republic" could not confirm the assaults on the airport, which has been closed for the past month because of the instability in the region.
The airport is one among very few areas in the Lugansk not controlled by the separatists, who have taken over most of the cities, set up numerous roadblocks and recently seized several checkpoints on the border with Russia.
The international airport at the nearby city of Donetsk briefly came under rebel control late last month.
The Ukrainian authorities took it back in severe fighting that cost the lives of dozens of fighters, mostly of Russian nationality, according to a report issued by Donetsk insurgents.