A provincial public health directorate official confirmed that the dead bodies of at least 9 people have been shifted to the hospitals along with at least 30 others who have sustained injuries.
Security forces and attackers are now fighting each other. More explosions were heard later coming from inside the building, the official added.
He said at least four attackers, armed with rocket propelled grenades and machine guns still appeared to be fighting police.
No one immediately claimed responsibility for the attack.
White House condemns Iran's 'reckless actions'
Confronted by Iranian-allied Hezbollah on its northern border, Israel also faces another enemy to the south with Hamas in Gaza. He warned that Israel will act forcibly to any response to its attacks.
The attack targeted the tax and revenue office of Nangarhar Province in the city center of Jalalabad on May 13. Both the Taliban and a local Islamic State affiliate have carried out numerous attacks in Nangarhar.
The Taliban and ISIS have made clear their intentions to disrupt the elections.
The Taliban recently launched their annual spring offensive, in an apparent rejection of a peace overture by the Afghan government.
Bladen County schools in session Wednesday; dozens of districts closed for rally
As of Friday afternoon, 14 local teachers put in requests for leave of absence for the day of the rally. We are on the right track, and I am pleased teachers will receive another raise next year.
But the Islamic State group has also stepped up their attacks in recent months, particularly in Kabul.
In Afghanistan, nine people were killed and more than thirty six injured in multiple blasts in Jalalabad on Sunday.
Afghan security forces have struggled to combat the Taliban and IS since the USA and North Atlantic Treaty Organisation formally concluded their combat role in the country in 2014, shifting to a support and counterterrorism mission.
Michael Owen states his prediction for Newcastle United v Chelsea FC
Let's be honest, they've messed it up. "You hear about rumours, but I'm just concentrating on Newcastle". Sunday's match is Chelsea's 1,000th in the Premier League since its formation for the 1992/93 season.