In one of the incidents, Taliban fighters attacked a security check post in the Muqur district of Ghazni province in southern Afghanistan, killing six police, according to district governor.
"Six of our local police were martyred after hours of clash with Taliban when they attacked their post early today," he said.
He added a second attack on a local police check post in Muqur wounded four police.
Also on Sunday, four Afghan border police were killed when their vehicle was blown up by a roadside bomb in eastern Nangarhar province that borders neighbouring Pakistan.
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"Today at around 10:00 am, a border police pickup truck hit a roadside bomb while on patrol in Mohamand Dara district of Nangarhar province," Ahmad Zia Abdulzai, Nangarhar provincial governor spokesman told AFP.
"As a result of the blast, four border police were killed." he said.
Afghan security forces are increasingly on the front line against the insurgents, and suffering heavier casualties, as NATO combat troops prepare to withdraw by the end of next year.