Reports say the suicide bomber apparently was targeting a district governor in Paktika Province.
In Herat Province, local police said militants attacked a police vehicle overnight, killing at least three officers.
There has been no claim of responsibility for the attack.
The violence follows clashes on April 24 in Oruzgan Province that left two suspected Taliban militants dead and four people wounded.
That fighting took place near northeastern Helmand Province, where NATO-led forces have been conducting a spring offensive against Taliban fighters within 150 kilometers of the strategic Kajaki hydroelectric dam.
(compiled from agency reports)
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