Police used water cannon and tear gas to prevent the peaceful protest from forcing entry to the airport, but deny using live ammunition.
Bullet casings have been collected to determine where the shots came from, but some eyewitnesses claim security forces did open fire.
Another eight people were injured in the clashes, which took union organisers by surprise.
“If we find casings from small weapons, then, as you know, the law-enforcement agencies do not use small calibres. We have big weapons,” said officer Kamran Fazal.
The Human Rights Commission of Pakistan called for a “prompt and credible” investigation into the deaths.
On Tuesday Prime Minister Nawaz Sharif passed a law banning airline employees from striking for six months.
The government says the partial sale of Pakistan International Airlines must be concluded by July this year.
At least two die as airline sell-off protests turn violent in Pakistan
03 February 2016
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The months of protests around the Pakistani government
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