Attaullah Khogyani, spokesman for the provincial governor of Nangarhar, confirmed a vehicle bomb was responsible for the attack in the town of Ghazi Aminullah Khan, on the main Torkham-Jalalabad road.
On Saturday a suicide assault on a gathering of Taliban, security forces and civilians in the province killed at least 36 people and wounded 65, Kamawal told AFP.
Their refusal to extend the three day hold on fighting comes as Taliban fighters were seen hugging and taking selfies with Afghan security forces and civilians as they all celebrated Eid.
Dozens of unarmed Taliban militants had earlier entered the Afghan capital and other cities to celebrate, coinciding with the end of the Ramadan fasting season.
In northern Kunduz province, Doctor Abdul Majhid said almost 2,000 Taliban were seen celebrating in the city, many of them with family and friends but also several were seen celebrating with Afghan Security Forces. Islamic State claimed responsibility.
Provincial police spokesman Shahpur Ahmadzai told The Associated Press that the Taliban were unarmed and no one was allowed into the city with weapons.
There were also rare scenes of impromptu diplomacy as the interior minister, Wais Barmak, met Taliban members on the outskirts of the capital and district governors broke bread with their Taliban "shadow" counterparts over lunch.
News of the bombing came just as President Ashraf Ghani, in a televised address, offered to extend his government's eight-day unilateral cease-fire, which is set to end Tuesday. "Everyone is exhausted of war and if our leaders order us to continue the ceasefire, we will hold it forever".
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A Kabul police spokesperson said many Taliban handed over their weapons as they entered the city, but in other cities, the insurgents walked through the crowds carrying weapons.
The Taliban's leader, Haibatullah Akhunzada, on Monday separately announced a three-day truce to mark the Eid holiday.
A senior member of the Taliban's shura or council said the group would meet on Sunday to discuss Ghani's offer and that the ceasefire could be extended if a date was set for the withdrawal of USA forces. They have also demanded the withdrawal of all foreign forces. Observers say it is unlikely that the militant group will engage in any negotiations, as they now have the upper hand on the battleground.
"The Taliban can always use a ceasefire as an opportunity to attack foreigners", one Western diplomat said.
Nangarhar is a province in eastern Afghanistan. Rampant corruption in the Afghan government and a long tug-of-war within the US-brokered national unity government has had a negative impact on the government's efforts to eradicate terrorism.
"The U.S.is prepared to support, facilitate and participate in these discussions", he added.
It's widely believed that including the Taliban as a minority party in a new Afghan Government will be part of any eventual peace deal.
The United States wants Pakistan, which it accuses of harboring Afghan Taliban commanders, to exert more influence on the group to bring it to the negotiating table. "We have no intention to extend the ceasefire", Mujahid told AFP in a WhatsApp message.