BBC quoted Afghan defence ministry while confirming the casualties here on Wednesday, At least nine militants were also killed, the minister added.
A number of hostages were seized in the 26-hour attack before Afghan forces retook the airport.
Final “mopping up operations” was under way, military officials said.
The Taliban said a number of suicide fighters managed to enter the base with weapons. They said “martyrdom seekers” launched “thunderous attacks on foreign and hireling personnel”.
The defence ministry statement said that a total of 11 insurgents took part in the attack. As well as nine killed, another was injured. Reports said a final gunman held out on his own for several hours before being killed late Wednesday.
Kandahar security officials put the number of attackers at 12, all of whom were killed.
At least 35 people were injured in the attack, the defence ministry said.
The raid was the latest in a series of battlefield victories by the Taliban who briefly seized the northern city of Kunduz in September.
The airport compound houses Afghan military and civilian sections as well as a Nato base.
Officials said the attackers initially managed to breach the first gate of the complex.
Kandahar army commander Sher Shah told reporters that radio intercepts had found that some militants were speaking in Urdu – a language more common in neighbouring Pakistan.
Afghan officials frequently blame Pakistan for unrest.
The statement by the Taliban claimed that they killed up to 80 soldiers. However, this figure could not be verified.
The latest violence came as Afghan President Ashraf Ghani called for help to defeat terrorism, at a regional conference in Pakistan.
Afghan Foreign Minister Salahuddin Rabbani, speaking at the conference, called on Pakistan to help restart stalled peace talks with the Taliban.—IANS