A CISF officer was also killed in the gunfight, while four security men were injured.
Tens of thousands of Afghan citizens have been waiting outside the airport since the Taliban took power in the country on August 15
No group has claimed responsibility for the attack but Islamic State militants operate in the area.
Sixteen others were wounded, including foreign and Afghan security forces, when a bomb-laden car exploded in the southern province of Kandahar.
The death toll in the suicide attack on a voter registration centre in the Afghan capital here on Sunday increased to 69 and the number of injured to 120, police said on Tuesday.
A suicide bombing outside a voter and ID registration centre in Kabul killed at least 57 people, and injured 112 people.
Afghan officials say a suicide car bombing in the southern Helmand province has targeted a police compound, killing one policeman and wounding two.