Sohrab Qaderi, a provincial council member in Jalalabad, said the attackers detonated a vehicle laden with explosives outside the government-run facility, with two smaller blasts following the initial position.
About 700 prisoners who escaped during the raid have been re-arrested, the Nangarhar governor's spokesman Attaullah Khogyani told AFP.
Khogyani says another 43 people have been wounded.
Over the three-day cease-fire weekend, Ghani said he had released an additional 500 Taliban prisoners as a goodwill gesture, bringing the total number of militants released to 4,600 out of the 5,000 pledged in the landmark agreement. AP's earlier story follows below.
At least 29 people have been killed in an attack on a prison in the eastern Afghan city of Jalalabad which saw more than 1,000 inmates try to flee. He expected the toll to rise.
Islamic State's Amaq news agency quoted a military source as saying its fighters had carried out Sunday's attack but gave no further details.
"What's really important about this attack is that these so-called Islamic State forces are the ones who claimed responsibility", said Latifi.
Last November, the Afghan and North Atlantic Treaty Organisation coalition forces defeated the ISKP, forcing hundreds to surrender along with their families, with a lot of them being Pakistani nationals who had infiltrated, four years ago, into Nangarhar province through the Durand Line -the border which Afghanistan has disputed since it was drawn by the British in 1893. It wasn't immediately clear if any prisoners were still at large.
Afghanistan's National Security Council said on Twitter that 317 prisoners had been freed since the holiday began on Friday.
The prison houses about 1,500 inmates, of which several hundred are believed to belong to the Islamic State group affiliate in Afghanistan.
The extremists have also battled the Taliban in the country, whom the USA overthrew following the 2001 American-led invasion after the September 11 attacks.
"Our mujahideen are not yet authorised to carry out attacks", Taliban spokesman Zabihullah Mujahid told AFP.
That deal was struck to allow the U.S.to end its 19-year involvement in Afghanistan, and calls on the Taliban to guarantee its territory will not be used by terrorist groups.
Both President Ashraf Ghani and the Taliban have signaled that protracted peace negotiations could begin once Eid-al Adha is over. Nevertheless, Washington and North Atlantic Treaty Organisation have already begun withdrawing troops in line with the deal.
ISIS claimed responsibility for the attack. The cease-fire expired at 12 a.m. Monday though it wasn't immediately clear if it would be extended as the USA pushes for an early start to intra-Afghan negotiations that have repeatedly been delayed since Washington signed a peace deal with the Taliban in February.