Several people have been injured as police responded with tear gas, water cannon and batons.
Police denied having opened fire on protesters, who broke through the cargo gate.
The two who died were workers of the company, hospital officials have said.
The violence came as hundreds of airline employees held the latest in a series of protests against the proposals to complete a partial sale of the airliner by July.
Police and paramilitary soldiers tried to keep the crowd from approaching the city`s Jinnah International Airport before shots were fired. The source of the gunfire was not immediately clear.
Senior police officer Kamran Fazal told reporters at the scene that officials had been collecting empty shells to determine where the gunfire had come from.
Pakistan`s Prime Minister, Nawaz Sharif, has invoked a law barring the airlines` employees from union activity for six months.
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