Seven police, including their commander, died when a suicide bomber detonated his explosives next to a group of officers in Logar province, south of Kabul.
"A suicide attacker on foot this morning targeted an Afghan local police commander in Puli Alam, killing him and six others," Abdul Hakim Eshaqzai, Logar's provincial police chief, told AFP.
The attacker, who was wearing a military uniform, struck as the commander was arriving at his office for a meeting.
Logar's media spokesperson Din Mohammad Darwish confirmed the attack.
Also on Monday, a remote-controlled bomb hit a police car in Jalalabad city in the east of Afghanistan, killing three police, Ahmad Zia Abdulzai, the provincial spokesperson told AFP.
Another roadside bomb blast left two civilians wounded in the capital Kabul.
The Taliban, who claimed responsiblity for the Logar and Jalalabad attacks, have stepped up attacks as the withdrawing Nato-led forces leave Afghan security forces to fight the insurgents on their own.
This year alone more than 4,600 Afghan soldiers and police have been killed in combat, a top US commander said last week, describing the losses as "not sustainable in the long term."
Nato will end combat missions in Afghanistan at the end of this year, with about 12,500 troops staying into 2015 on a training and support mission.
On Sunday, a suicide bomber walked into the offices of Kabul's police chief and detonated his explosives, killing a senior aide.
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These cowards can only kill their own countrymen.