NATO said Monday that another two service members died in an insurgent attack in eastern Afghanistan the previous day, raising the death toll to five.
In another attack, an insurgent rocket sparked a huge blaze inside an American base.
The international military coalition did not provide details on Sunday's attack or the nationalities of the service members. Though a number of nations have troops in the east, the majority of the forces are American.
NATO announced three of the deaths Sunday, then added two more on Monday.
The deadly strike came a day after Taliban fighters stormed a NATO base in eastern Afghanistan, showing the insurgents' determination to stage attacks despite a surge of U.S. troops and firepower.
In eastern Kunar province on Monday, an insurgent rocket struck inside a U.S. base near the provincial capital of Asadabad, sparking a fire that destroyed six armoured vehicles and an ambulance, NATO and Afghan officials said.
Associated Press Television News video showed plumes of black smoke rising from inside Camp Wright through much of the morning, with flames shooting up into the air. Provincial police Chief Khalilullah Zaiyi said Afghan firefighters were dispatched to help quell the blaze.
Taliban spokesman Zabiullah Mujahid claimed responsibility for the attack.
The base came under attack from gunfire and rockets early in the morning and one rocket hit a fuel container, starting the fire, NATO said in a statement. There were no coalition injuries.
The fire was contained by late morning, NATO said. The six armoured vehicles that were destroyed were Mine Resistant Ambush-Protected vehicles, known as MRAPS, which can cost as much as $1 million US each.
Tens of thousands of Afghan and coalition troops are pressing insurgents throughout southern and eastern Afghanistan, and militants are retaliating with attacks on government workers and others aligned with the international troops.
The number of coalition service members who have died in Afghanistan this month has reached 33.