The blast on Sunday outside the regional governor's office in Jalalabad city came just a day after a suicide bomber killed at least 36 people, including civilians, government forces and Taliban fighters, at an Eid gathering in the same province.
No group has claimed responsibility for Sunday's attack but the one on Saturday was claimed by the local affiliate of the Daesh (also known as ISIL or ISIS) group.
Najibullah Kamawal, Nangarhar provincial health director, put the death toll from Sunday's blast at 18 with 49 wounded, Al Jazeera reported.
"Some of the wounded are in a serious condition," Kamawal added, suggesting the death toll could rise.
Separately on Sunday, the Taliban ruled out an extension of a ceasefire agreement with Afghanistan's government that was due to end in the evening.
The two sides had agreed to stop operations against one another for the Muslim holiday of Eid, which started on Friday.
On Saturday, Afghanistan's President Ashraf Ghani announced the extension of the truce without specifying an end date and called on the Taliban to do the same.
Ghani also said that in the spirit of Eid and the ceasefire, the attorney general's office had released 46 Taliban prisoners.
The possibility of a peace deal between the Afghan government and the Taliban comes as ISIL establishes its presence in the country.
Omar Samad, a former adviser to the chief executive of Afghanistan, told Al Jazeera that the suicide bombing on Saturday was a reminder to everyone in the country, including the Taliban, of the "existentialist threat on our doorstep".
"What we saw today is a reminder that ISK (the ISIL branch in Afghanistan) is a potent threat, that something needs to be done about it," Samad said, speaking from Washington, DC.
"Maybe the Taliban and the Afghan government can come to terms on how to deal with the Daesh," he added.
"That could be an historic point for maybe a dialogue between the two sides. If that happens then I think that Afghanistan has better days ahead."
The Taliban's decision to hold a ceasefire with the government was the first time it had reached such an agreement since the 2001 invasion of the country by a US-led coalition.