"Unfortunately, 13 people have been killed and 20 others injured in a suicide attack that targeted a police minivan today," said provincial spokesman Abdul Zia Ahmadzai.
The attack happened at around 4:45 pm (1215 GMT) in the eastern province of Nangarhar, just outside the city of Jalalabad and a few kilometres from Jalalabad airport.
The suicide bomber is thought to have rammed his explosive-laden car into the bus carrying police.
The attack was claimed by the Taliban. Its spokesman Zabiullah Mujahid said: "One of our mujahedeen carried out a martyrdom attack on a bus carrying police trainers in Nangarhar province today.
"The bus was totally destroyed and 25 police trainers were killed. Unfortunately, two civilians were also martyred." The Taliban are known frequently to exaggerate the scale of their attacks.
The strike came on the same day that 12 people died during a violent protest in Takhar province, northeast Afghanistan, against a NATO-led raid which left four people dead.
The protesters and President Hamid Karzai, who condemned the operation, said the four dead were civilians. But the International Security Assistance Force (ISAF) said they were insurgents.