In Kabul, two rockets fired from the east of the Afghan capital hit inside the city but caused no casualties.
In Ghazni, police chief Mohammad Zaman says the insurgents targeted a security post in the district of Waghaz early on Monday. He says along with the four killed, two policemen were wounded in the attack.
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Zaman says the attack set off a heavy gunbattle that lasted hours. He says the Taliban were "defeated with heavy causalities."
Najib Danish, spokesman for the Ministry of Interior, says the target of the Kabul attack, also on Monday morning, was not immediately clear.