Flights from Kandahar airport were cancelled when rockets hit the runway, an official said, as the Taliban pressed on with their sweeping offensive across the country.
The air strikes, carried out over the last two days, mark a rare military intervention by the United States since it signed an agreement on troop withdrawal with the Taliban in February.
Officials say the suicide bomber targeted election candidate Saleh Mohammad Asikzai's campaign office in the southern city of Lashkar Gah in Helmand province. There was no immediate claim of responsibility for the attack.
The assault by the US on its allies in Afghanistan also killed two commanders. NATO has ordered a probe into the incident which Afghan officials said happened as security forces were clearing Taliban elements from a village in Helmand province.
Some 60 people were also wounded in the assault on a bank in the provincial capital as civilians and members of the security forces were queuing to withdraw their salaries.
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