The soldier with Nato's International Security Assistance Force [ISAF] was killed on Monday when a bomb struck a military vehicle travelling through the southern province of Kandahar, Nato said on Tuesday.
"One ISAF soldier died and two were injured when the vehicle they were travelling in was struck by an improvised explosive device [IED] in the Panjwayi district of Kandahar yesterday," a statement read.
An Afghan soldier was killed the same day when another IED struck a military patrol in the Gereshk area of neighbouring Helmand province, Andre Salloum, an ISAF spokesman said.
"A vehicle went over an IED which was on the road. One vehicle was damaged and had to be destroyed," he said.
In the eastern province of Khost meanwhile, Taliban fighters attacked a highway police post just after midnight on Monday.
Two attackers and a policeman were killed in an ensuing gunfight, provincial police said
Several thousand ethnic Pashtuns rallied in a Pakistani town near the Afghan border on Tuesday, accusing Pakistan of meddling in Afghanistan's affairs.
The protesters, Pakistani Pashtuns and some Afghan Pashtun refugees, accused Pakistan of providing sanctuary to Taliban fighters.
"We demand the government of Pakistan stops playing its game in Afghanistan," Hamid Khan Achakzai, a leader of a Pakistani Pashtun nationalist party and a former member of parliament, told the rally in the southwestern town of Chaman.
"This duplicitous policy poses serious danger to the entire world," Achakzai said.
Pashtuns live on both sides of the rugged Afghan-Pakistani border.
Afghan complaints that Taliban fighters are operating from safe havens on the Pakistani side have seriously strained relations between the neighbours this year.