The assault on the Kandahar air field comes just days after two Taliban attacks on US and Nato forces in Afghanistan.
The group says it has now begun its "summer offensive" and will increasingly hit foreign troops.
Codenamed Al Fatah, or victory, the operation anticipates a planned summer offensive by coalition forces in Kandahar, aimed at driving the Taliban from their traditional heartland.
Al Jazeera's Adam Raney reports.
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