(Reuters) - Bombs exploded in three cities in Afghanistan on Monday killing at least 10 policemen, officials said, a day after a Taliban suicide bomber blew himself in Kabul's police headquarters killing one person.

The Taliban were ousted from power in 2001 by U.S.-led forces and they have been fighting ever since to oust foreign troops and the U.S.-backed government, even as most foreign forces are pulling out by the end of this year.

The militants claimed responsibility for two of the attacks, which killed the policemen, seven of them in the eastern province of Logar province when a suicide bomber blew himself up at the provincial police headquarters.

In Nangarhar province, also in the east, three policemen were killed in the city of Jalalabad by a bomb planted in a rickshaw, officials said.

It was not clear who was behind the third blast, in Kabul, caused by a bomb planted in a flower bed near a university. It wounded three people.

Taliban violence has increased as foreign troops have withdrawn, leaving Afghan security forces to fight alone or with limited air support.

The police and army have suffered heavy losses as a result. A top U.S. commander in Afghanistan recently said the casualty rate among Afghan government forces was "not sustainable".

The Taliban also claimed responsibility for the Sunday suicide bomb attack on police headquarters in the capital.