The attack was apparently targeting the airport headquarters of NATO and included assault rifles, a large bomb and rocket propelled grenades.
Two civilians were injured in the attack, but security forces from Afghanistan were able to kill all seven Taliban after an hour of fighting.
The attack was one of three, during Monday morning, on state facilities, by Taliban insurgents in different places in the country.
In another, six militants wearing vests with suicide bombs attempted to storm a council building in the province of Zabul in southern Afghanistan. Three others attempted an attack on a police headquarters on the outskirts of Kabul.
A spokesperson for the Interior Ministry said that the Zabul attack had wounded 18 people, three of which were police officers.
A car bomb exploded outside the provincial council building in Qalat, however security forces were able to killed the insurgents prior to them entering the building.
Just outside of Kabul, one attacker was killed by police and two others were arrested when they tried to storm the police headquarters in the district of Surobi.
The attack in the capital was the third in less than a month where insurgents have attempted an attack that was large in size against targets that were high-profile.
Hamid Karzai, the President of Afghanistan said the government would not allow attackers to deter them. He called the terrorist attacks cowardly against the people of Afghanistan.
Karzai was in Qatar visiting when the attack in Kabul took place. He was discussing the peace process that has stalled and the possibility of opening an office for the Taliban in Doha.