The rockets landed on the military side of the airport, which includes a large NATO base as well as a separate terminal for civilian flights to cities such as Dubai, New Delhi and Istanbul.
"Three rockets have landed inside the military garrison of Kabul airport from an undisclosed location," a statement from Kabul police said. "Part of the area where the rockets landed has caught fire."
Mohammad Yaqub Rassouli, head of the airport, said that firefighters rushed to put out the blaze in a hanger containing spare parts as military flights were halted.
Taliban spokesman Zabihullah Mujahid in an email message sent to AFP claimed the responsibility for the attack on the airport, which has been targeted several times in recent years.
"There is loss of life and financial losses to the airport, and several planes were torched," the Taliban said. The insurgents often exaggerate the impact of their attacks.
The strike comes a day after a Taliban suicide bomber in Kabul killed eight military officers travelling on a military bus.
The Afghan capital has been relatively peaceful since the presidential election on June 14, though there have been street demonstrations as politicians are locked in a dispute over vote fraud.
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