Interior Ministry spokesman Najib Danish says one policeman was killed and another five were wounded.
Reuters reports that two loud explosions and gunfire were heard in proximity of the Interior Ministry compound and that police inside reported that the facility was under attack by militants.
Two of the attackers detonated their explosives, allowing eight others to pass through an outer gate at the ministry where they traded fire with security forces before they were eventually killed.
In eastern Logar province, suicide bombers attacked a police station in the morning, killing at least three police officers, including the station's commander and the deputy director of traffic police for the provincial capital, Pul-e Alam, local media reported.
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Danish said 10 attackers were involved; three with suicide vests and seven others armed with weapons and wearing military style uniforms.
"It was 5 in the morning when the Taliban exploded a auto bomb near the First District Police Headquarters and three suicide attackers entered the building", Mr. Ahmadzai said.
After pushing out fighters in Farah, Afghan and United States forces continued to pursue them, Nicholson told reporters at the Pentagon via video link.
Hundreds of Afghan forces have been killed in the Taliban attacks, raising further questions about the viability of holding long-delayed parliamentary and provincial council elections slated for October ahead of next year's presidential vote.
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There have also been numerous attacks on government buildings and at police checkpoints. He said all three were shot and killed by security forces within minutes of the initial attack, adding that a number of nearby homes were damaged.
It is estimated that about 15 million people - half the population - are living in areas that are either controlled by the Taliban or where the Taliban are openly present and regularly mount attacks.
Also on Wednesday a vehicle bomb in the southern city of Kandahar went off inside a garage where Afghan army vehicles were being repaired, killing three mechanics and wounding 13 people, governor's spokesman Daud Ahmadi said.
Mohammad Salim Roodi says the attack took place in Girishk district when the police tried to stop a suspicious vehicle outside the governor's compound. No group immediately claimed responsibility.
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