Spokesman Omer Zwak of southern Helmand province said the suicide car bomb attack happened in the provincial capital city of Laskar-Gah and killed four civilians. He added that another 15 were wounded.
Zwak had no details about how the attack was carried out but said there were no immediate reports of casualties among coalition forces. They usually drive in heavily armoured vehicles.
Spokesman Abdul Rahman Zhawandai of western Farah province said a rocket fired at a parking lot used by truck drivers carrying fuel for the coalition hit a fully laden vehicle, which immediately caught fire. The ensuing blaze killed six Afghan drivers and wounded another 10.
The coalition imports all the fuel it uses in the country and it is transported by Afghan civilian contractors.
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"The fire destroyed so many trucks because we have no way to fight them," he said.
The Taliban claimed responsibility for the attack in an email and said it was part of their campaign against the coalition and government of President Hamid Karzai.
They have so far unsuccessfully tried to retake territory in their traditional southern and eastern heartlands.