The roadside bomb struck the soldiers' vehicle in Nuristan province, NATO said. The two wounded soldiers were taken to a U.S. military facility in Asadabad in neighboring Kunar province.
NATO did not release the nationalities of the soldiers, but U.S. troops are the primary NATO component in eastern Afghanistan.
NATO troops on Monday fought insurgents in southern Afghanistan for six hours in a firefight that killed 55 militants and one NATO soldier from the alliance's International Security Assistance Force. Twenty militants were wounded in the battle in Zabul province, NATO said.
The nationality of the soldier killed Monday was also not released, though many of the Western troops in Zabul are also American.
Afghanistan has seen a sharp rise in violence the last several months, particularly in the southern and eastern provinces near the border with Pakistan. Militants have been increasingly using roadside and suicide bombs in their attacks against Western and Afghan security forces.
In Ghazni province, meanwhile, a suicide attacker detonated explosives Tuesday outside the Andar district police chief's office, killing one officer and wounding another, said Gen. Abdul Ghafar, the provincial police chief. Ghafar said the attacker tried to enter the chief's office but was stopped by police.
Two NATO soldiers were also injured in the attack, said Maj. Luke Knittig, a spokesman for NATO's ISAF.
Britain's Ministry of Defense released
Commando Royal Marines arrived to take over command of the area from another British contingent, in an operation dubbed 'Operation Silica', according to the Ministry.
The advance party from 'K' Company — 42 Commando Royal Marines arrived in a Chinook helicopter then patrolled through the streets of Now Zad, a district in the North of Helmand province which houses local government and the local police force.
Just as the Fusiliers started their handover a brief fire fight began when suspected Taliban fighters were spotted.
The British soldiers and Afghan police forces responded with machine guns from a defensive position which dominates the area.
The fire fight lasted 40 minutes, according to a statement released by the Ministry.
No casualties had been reported by Tuesday afternoon.
The British force being replaced in Now Zad had been there since July 10, 2006, with a mission to defend the strategic hilltop compound and the Afghan police force in the area.
The hill has been the subject of increased fighting over the past four months, according to the Ministry.
NATO took command of southern Afghanistan from the United States on July 31, and the 32,000-strong NATO-led force took command of security operations in all of Afghanistan last month.
The alliance has been battling resurgent Taleban militants in the south and east in the worst increase in violence since the 2001 U.S.- led invasion ousted the Taliban in the wake of the September 11 attacks.