The deadliest attack was a suicide car bombing just after sunrise in the eastern city of Jalalabad that killed two guards at an intelligence agency office.
In that attack, a car approached the gate of the compound used by the National Directorate of Security and exploded, killing two guards and wounding three others, said regional government spokesman Ahmad Zia Abdulzai. The building was damaged in the attack, he added.
Taliban spokesman Zabiullah Mujahid claimed responsibility for the bombing.
Shortly before the Jalalabad attack, an assailant detonated a van packed with explosives at a highway police checkpoint in Logar province, also in the east. That explosion wounded three police officers but no one was killed, said Deputy Police Chief Rais Khan Abdul Rahimzai.
In Kabul, meanwhile, local television stations showed footage of the aftermath of a shootout in which Afghan security forces killed a man who appeared to be an insurgent attacker. In the footage, intelligence agents step over the body of the man as they inspect the 4x4 vehicle he was driving. Officials declined to comment on the incident.
Later in the morning, a man wearing a suicide vest blew himself up outside the police headquarters for Baraki Barak district in Logar province. The man was stopped by police as he tried to force his way into the building, but still managed to detonate his vest, said Din Mohammad Darwesh, the provincial government spokesman.
One policeman was wounded in the Baraki Barak attack, Darwest said.