Wednesday's victims were among personnel preparing to unload supplies from a Chinook helicopter at the forward operating base at Shkin in Paktika province, the military said in a statement.
The attack came as Afghan and US-led forces arrested five men suspected of being Taliban rebels responsible for a deadly attack on a Pakistani-owned fuel tanker on Tuesday.
The tanker was delivering petrol to a US base in southern Afghanistan, police said.
The truck's Pakistani driver and assistant were killed in the assault late on Tuesday in Spin Boldak district, which is next to the border between Pakistan and Afghanistan.
Afghan and UN-backed multinational troops fanned out across the area on Wednesday morning, searching for the attackers. The five were arrested on Wednesday in a village in the area, district police chief Mohammed Raz said.
Abdul Latif Hakimi, a purported Taliban spokesman, claimed responsibility for the killings, saying that anyone working for the United States would be targeted.
"We will continue to attack those who supply Americans - we've got to cut off the Americans' supply routes"
Abdul Latif Hakimi,
"We killed the drivers," he said by satellite phone from an unknown location. "We will continue to attack those who supply Americans - we've got to cut off the Americans' supply routes," Hakimi said.
In recent months, Taliban-led rebels have stepped up attacks on Afghan and UN-sanctioned multinational forces as well as softer targets associated with President Hamid Karzai's government.
The security forces have hit back, killing more than 200 suspected rebels since March.
Twelve US military personnel have been killed in a wave
of clashes, blasts and rebel ambushes in Afghanistan since late March.