The NATO service members were carrying out the operation with Afghan troops in Kandahar Province when a roadside improvised explosive device was detonated near them, Khaama Press reported.
NATO confirmed that four soldiers were killed in the incident, while an unnamed military official said the deceased troops were American.
The International Security Assistance Force said in a statement that the soldiers were killed "by enemy forces during a partnered operation."
The New York Times reported that this was the NATO coalition's biggest loss of life in a single incident since June.
The last time as many as four coalition troops were killed in Afghanistan was on June 18, when militants launched a rocket at the Bagram Air Base north of Kabul.
In a separate incident on Saturday, a NATO soldier was shot and killed "when an alleged contracted security guard shot the service member," the coalition said.