The three killed were Czech soldiers, the country's military confirmed.
The Taliban claimed the attack, which took place near Charakar, the provincial capital of the Parwan province.
US Army General John Nicholson, the commander of US and Nato forces in Afghanistan, said: “My thoughts and prayers, along with those of all of the 41-contributing Resolute Support nations, are with the families and friends of our fallen and wounded service members, and our injured Afghan brothers and their families.
“Their sacrifice will endure in both our hearts and history, and further strengthen our resolve.”
Czech Defence Minister Lubomir Metnar also offered his condolences.
The Czechs had recently approved a plan to deploy 390 soldiers in Afghanistan until 2020, up from the current 230, as part of the Nato-led Resolute Support mission.
Nato formally concluded its combat mission in Afghanistan in 2014, but some 16,000 US and other Nato soldiers are providing support and training to Afghan troops and carrying out counterterrorism missions.
Last month, the Taliban struck a Nato convoy with a suicide car bomb in the eastern Logar province. The attack killed two civilians and damaged a Nato vehicle.
Elsewhere in Afghanistan, the Taliban attacked a newly constructed district headquarters in the southern Uruzgan province early on Saturday, killing four Afghan soldiers, according to Mohammad Maruf Ahmadzai, the provincial police chief.
Mr Ahmadzai said nine Taliban fighters were killed in the ensuing gun battle.
The Taliban claimed the attack and said they captured soldiers alive.
Both the Taliban and a local Isis affiliate regularly target Afghan security forces. The Isis affiliate has also carried out several attacks targeting the country's Shiite minority.
Isis claimed a suicide attack two days earlier on a mosque in the city of Gardez, south of Kabul. That attack killed at least 29 people and wounded another 81.
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