NATO did not provide any further details on the attack that killed the service members, its location or their nationalities. It was not clear if the two attacks were related.
The Afghan officials said the attack in the south took place in Uruzgan province on Sunday afternoon.
Fareeb Ayal, a spokesman for the police chief of Uruzgan province, said a suicide bomber blew himself up at a police checkpoint near a marketplace in Tarin Kot, the provincial capital.
Ayal said a NATO convoy was at the checkpoint at the time of the explosion. He said six children were wounded, two of them critically. He said there were some NATO casualties too, but he didn't have details.
Salim Ahsas, a spokesman for the Afghan National Police in the south, said three NATO troops were wounded. Taliban spokesman Qari Youssef Ahmadi said the Taliban were behind the attack.
The latest violence came as world leaders, weary of war, are to tackle Afghanistan's post-conflict future - from funding for security forces to upcoming elections - at a NATO summit in Chicago that opens Sunday.