More than 20 others were injured after the rockets landed in residential areas close to the airport.
Security forces at the airport are reported to have fired back.
Peshawar is located on the edge of Pakistan’s tribal region, the major sanctuary for al-Qaida and Taliban militants.
Women and children are among the dead and injured.
Three rockets landed in residential areas close to the airport.
The airport is used as a base by the Pakistan Air Force as well as for commercial flights.
It is not clear if the militants entered the airport.
The information minister of Khyber Pakhtunkhwa province told journalists that the airport had been cordoned off but the situation was still unclear.
It is not yet known who was responsible for the attack.
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