The battle took place inside a building which houses the state accounts office. Following the explosion, several gunmen opened fire and engaged in clashes with the security forces near the government facility.
No one had claimed responsibility for the attack at the time of filing this report.
Most have been in capital city Kabul, but in January gunmen attacked an office of aid group Save the Children in Jalalabad, killing at least five people and wounding 25.
Afghanistan has always been suffering from political, social and security instability, primarily due to the hostilities between government troops and the Taliban radical movement, which seeks to establish strict Sharia law in the country.
At least four people had been killed and 20 wounded, a spokesman for the Nangarhar provincial governor told the media.
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Security forces are fighting back, he said, adding that six civilians have been killed.
Earlier, he said the attack had been carried out by four attackers and that there had been two explosions.
Inamullah Miakhial, a Nangarhar hospital spokesman, also confirmed the dead toll and said that more than 40 wounded people are undergoing treatment at the hospital.
"I saw two rickshaw drivers on the ground with their arms blown off", said Khan Mohammad, a local resident who saw the initial blasts and the start of the gun battle.
However, the Taliban is now taking part in its annual spring offensive and has launched a number of attacks in recent weeks.