KABUL—Less than a day after the assassination of one of Afghanistan’s most powerful anti-Taliban leaders, the Kabul government on Friday postponed voting in Kandahar province for this weekend’s crucial parliamentary elections.

With balloting for the 249 seats in the lower house of parliament scheduled for Saturday, top security officials decided in an early-morning meeting in the capital to put off polls for a week in Kandahar, one of country’s most influential provinces, said Shah Hussain Murtazawi, deputy spokesman for Afghan...