Twelve bodies had been taken into the main regional hospital in Jalalabad city, 125 kilometres from the capital Kabul, said Ahsanullah Shinwari, the head of the hospital.
Another 38 people were wounded, most of them in critical condition, he said.
The recruits were travelling in a bus overnight on the outskirts of Jalalabad — the capital of Nangarhar province.
Initial reports indicated that an attacker on an explosives-laden motorcycle rammed the bus, according to Ahmad Ali Hazrat, chief of the Nangarhar provincial council.
No group has yet claimed responsibility. Suicide attacks regularly take place in Jalalabad, as the province is home to a number of anti-government insurgent groups.
Earlier in Kabul, at least one person was killed when a bomb ripped through a bus carrying Education Ministry employees to work.
Interior Ministry Spokesman Sediq Sediqqi said five people were wounded in the blast, caused by a magnetic bomb attached to the bus.
Rahim Gul, the assistant bus driver, gave a higher death toll, telling The Associated Press that two employees were killed.
No group immediately claimed responsibility for that attack. The Taliban frequently use roadside and so-called sticky bombs, as well as suicide attacks against Afghan security forces and government employees across the country.
Such bombings regularly take place in Kabul, though the Afghan capital has not seen a major attack in several months.