At least three rockets struck Kandahar airport in southern Afghanistan overnight, Afghan officials said on Sunday.
Reuters news agency cited the Taliban as saying it was responsible for the attack with the aim of stopping enemy airstrikes.
A Taliban spokesperson told the news agency that the airport was being used as a "center" to conduct airstrikes against the group.
A portion of the runway was damaged, forcing officials to suspend all flights. Services will likely resume later on Sunday.
There were no immediate reports of casualties.
What is the relevance of Kandahar?
Kandahar airport is also home to an Afghan Air Force base, which is vital for providing the logistics and air support needed to keep militants from overrunning Afghanistan's second-biggest city.
Though militants have made rapid territorial advancements in rural areas, the group has not made gains in major cities.
But it is fast encroaching on key centers.
It picked up fighting in two other provincial capitals in recent weeks, raising fears about how long government forces can hold out.
On Friday, militants briefly attacked a UN compound in the western city of Herat, killing one guard and injuring others. The attack was widely condemned by countries from around the world.