The vehicle carrying border police officers struck the explosive device in Achin district in eastern Nangarhar province, an Afghan official says.
Abu Saad Erhabi was the fourth Daesh leader in Afghanistan to be killed since July 2017.
A suicide bomber struck in Afghanistan's eastern city of Jalalabad on Sunday, killing at least 18 people in the second attack in as many days, as Taliban announced they would not extend their three-day ceasefire with the Afghan government.
The attack, which killed at least two and wounded 12 people, comes days after an attack on Kabul's Hotel Intercontinental. Aid agency temporarily suspends operations.
An American soldier was killed and four other soldiers were wounded in the January 1 battle in the Achin district of Afghanistan's Nangarhar province, a military statement said.
The Pakistan Army says it has recovered a Canadian, his US National wife and their three children from "terrorist custody" after receiving intelligence from US officials.
The latest incident claimed by Taliban took place in Nangarhar province. There've been many cases when Afghan soldiers or police turned their guns on international troops in so-called "green-on-blue" attacks.
The attack came hours after a policeman killed five colleagues in their sleep at an outpost in eastern Nangarhar province.
The US military on Thursday dropped its most powerful non-nuclear bomb, the Massive Ordnance Air Blast (MOAB), in Nangarhar, Afghanistan, targeting the caves held by Daesh.
The attack targeted Shia worshipers who had gathered at the mosque to mark the end of a 40-day mourning period for the death of Imam Hussein, the grandson of the Prophet Muhammad.
As the militant group steps up its attacks in the country, Afghans still see Daesh as a mysterious foreign entity whose makeup and intentions remain unclear to both officials and locals living under the group's rule.
At least six civilians killed and several others injured as suicide bomber attacks meeting in Jalalabad.
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