At least three Afghan policemen were killed when suicide bombers attacked a police training centre in the east of the country, officials say.
Police said two bombers also died in the raid on the base in Paktia province where dozens of men were being trained.
Two more suicide attacks took place in Kabul and Kandahar, police said. The Taliban claimed all three attacks.
Several policemen were wounded in the Kabul incident. In Kandahar, three people, two of them women, were hurt.
Wave of attacks
Paktia, close to Pakistan's lawless tribal areas, is said to be a stronghold for several militant groups.
According to police, four men with explosives tied to their bodies tried to enter the police training compound in Paktia and were challenged by security forces.
The first attacker blew himself up outside the base, killing three policemen and injuring another three who were guarding the front gate, police said.
A heavy exchange of fire followed in which the second attacker was killed. Police said the remaining two attackers managed to escape, the BBC's Bilal Sarwary reports from Kabul.
In the Kabul attack, a truck laden with explosives blew up outside the district governor's office. The attacker was killed and several policemen were injured, officials said.
In the third incident, police killed a suspected militant who was trying to enter a police station in the southern city of Kandahar. Officials said the man was wearing an explosive belt.
The attacks come a week after Taliban militants killed six security personnel in an attack on a police training centre near Kandahar. Three gunmen also died.
Tens of thousands of Afghan police and troops are being trained to assume full security control once Nato leaves.
Afghan forces are frequently targeted by the Taliban and their allies, who want to oust the Western-backed government of Hamid Karzai in Kabul.