KABUL—As the body of one of Afghanistan’s most vaunted anti-Taliban fighters was laid to rest on Friday in the southern city of Kandahar, the implications of his assassination reverberated across the country, deepening the sense of political uncertainty.

Afghan officials announced that voting in parliamentary elections set for Saturday would be postponed for a week in Kandahar province, where the revered and controversial Gen. Abdul Raziq served as police chief. He and the province’s intelligence chief were killed Thursday...