The AFP news agency cited anonymous Isaf officials as saying that a sixth soldier had died in an accidental explosion, and that all the dead were Americans. However, Isaf's policy is not to announce the nationalities of killed forces.
Nato forces also issued a statement on Saturday admitting troops accidently killed six civilians while battling Taliban fighters earlier in the week.
A brief statement released by the mission's headquarters said that the civilians died on Thursday under artillery fire from a Nato unit in Paktia province, south of Kabul.
Nato's admission comes a day after the force said it was responsible for accidentally killing five Afghan soldiers in a botched airstrike.
The incident occured in Andar district of Ghazni province, where the Afghan soldiers were launching a pre-dawn ambush against fighters.
Aircraft from the military alliance began firing on them without warning, an Afghan defence ministry official said. Nato blamed the attack on a communication error.
A statement, also issued on Friday, said a joint investigation determined that the Afghan army unit gave the wrong location to international forces when it reported it would be operating in Ghazni.
The two incidents would likely hurt efforts by international troops to gain the trust of the Afghan people and improve co-ordination with Afghan security forces in hope of handing over more responsibility for security to them, nearly nine years into the war.
Hundreds of Afghans took to the streets of Mazar-i-Sharif on Saturday to protest against civilian deaths.
The protesters chanted slogans against foreign forces and Hamid Karzai, the Afghan president, after US troops killed two civilians and arrested three others during a pre-dawn raid on Wednesday in the northern city's outskirts.