No one immediately claimed responsibility for the attack but the Taliban recently have staged a series of high-profile bombings ahead of the June 14 runoff in the country's presidential election.
The attack on the police base in eastern Behsud district took place late yesterday, said Ahmad Zia Abdulzai, the spokesman for the governor of Nangarhar province.
A suicide car bomber first blew himself up by detonating his vehicle at the entrance to the parking lot, then two other attackers then stormed in, shooting at the security forces, he said.
Meanwhile today, a group of suicide bombers stormed a court building in eastern Jalalabad, the capital of Nangarhar province, Abdulzai said.
Afghanistan's Interior Ministry said in a statement that a suicide bomber attacked the building's entrance, allowing three other attackers to get inside.
"All three attackers were shot and killed by police forces before they were able to detonate their suicide vests," the statement said.
The attack wounded four people, including three civilians and one police officer, the statement said.
Last Friday, Abdullah Abdullah the front-runner in the election narrowly escaped assassination when two suicide bombers attacked his convoy during a campaign event in the capital, Kabul.
The blast killed at least 10 people, including three in Abdullah's entourage, and wounded dozens.
The attack heavily damaged the front of Abdullah's armoured car, destroyed several vehicles and storefronts and left the street littered with twisted metal and other rubble.
No one has claimed responsibility for that attack either.