Attahullah Khogyani, the spokesman for the provincial governor, said the attackers killed at least four victims and that at least 20 other people were wounded.
A public office in eastern Afghanistan came under an armed attack on Sunday, officials said.
Afghan security forces surrounded the area and were still battling the gunmen hours after the initial explosions.
It was the latest in a series of high-profile attacks that have killed and wounded hundreds of civilians in Afghanistan this year and put heavy pressure on the Western-backed government of President Ashraf Ghani.
Jalalabad is the capital of restive Nangarhar, which borders Pakistan. There were multiple blasts as they fought off security forces in a gunbattle that lasted much of the day.
No individual or group including the Taliban militants has so far claimed responsibility behind the attack.
Exit polls is 'entertainment for the next 2 days': Siddaramaiah
Till about 3 pm, approximately 53% voter turnout was reported in the single-phase Karnataka elections , as per poll officials. On a related note, the Karnataka Assembly has 224 seats and a party or an alliance needs 113-seats to form the government.
Earlier, he said the attack had been carried out by four attackers and that there had been two explosions.
The Taliban recently launched their annual spring offensive, in an apparent rejection of a peace overture by the Afghan government.
Security forces and attackers are now fighting each other.
Their Operation Al Khandaq will target USA forces and "their intelligence agents" as well as their "internal supporters", a Taliban statement said on April 25.
Last month, an Islamic State suicide bomber killed at least 57 people, including women and children, and wounded 119 outside a voter registration centre in the Afghan capital Kabul in the latest attack on election preparations.