Bombs have struck three Afghan cities, including the capital Kabul, killing at least 10 policemen.

In Kabul, a magnetic bomb planted in a flower bed near a university wounded three people, while seven police were killed in eastern Logar province when a suicide bomber blew himself up at the provincial police headquarters.

In eastern Nangarhar province, three policemen were killed by a bomb planted in a rickshaw, officials said.

Monday's blasts came a day after a Taliban suicide bomber penetrated police headquarters in Kabul killing a senior police officer. Taliban fighters reportedly claimed responsibility for Sunday's attack in the capital.

Kabul is regularly hit by Taliban bombings, with the military, police and government officials among those targeted despite heightening security with multiple checkpoints, guard posts and armed convoys.

In the last major blast, four Afghan soldiers were killed and around a dozen people - including six civilians - wounded when a roadside bomb planted by the Taliban exploded on October 21.

Afghan soldiers and police have taken on the lead role in thwarting the Taliban, but national stability could be at risk as US-led NATO troops pull out.

This year alone more than 4,600 Afghan soldiers and police have been killed in the fighting, according to recent US figures.