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The attack in the Qarabagh district of Ghazni province lasted about an hour and started when the Taliban launched two rockets at the district's administrative headquarters before opening fire on a police checkpoint nearby.
Police shot back, triggering a gun fight, but insurgents did not get inside the compound, Ghazni police chief Dilawar Zahid said.
"Four militants and a policeman have been killed in the clash," Zahid said.
Taliban spokesman Zabiullah Mujahid claimed that eight policemen were killed in the clash.
The attack came after 22 people died in a gun and suicide attack on the compound of the governor of Parwan province, just north of the Afghan capital Kabul.
Copyright AFP (Agence France-Presse), 2011