The Taliban quickly claimed responsibility for the crash, but the coalition said in a statement to The Associated Press: "Taliban's claims are false."
It said the cause of the crash was being investigated by emergency crews that rushed to the site, but there was no sign of insurgent activity in the area at the time.
Capt. Luca Carniel, a coalition spokesman, said the aircraft crashed from a low altitude right after takeoff.
The coalition did not identify the victims, the type of aircraft involved, or the company that owned it.
In another development, President Hamid Karzai accused U.S. forces of killing four civilians and wounding one in the eastern province of Nangarhar on Sunday after an American' convoy was attacked by insurgents.
In a statement issued by his office, Karzai "strongly condemned the killing of innocent civilians."
The U.S.-led military coalition said it was still investigating the weekend clash, which left four soldiers with minor injuries and damaged a patrol vehicle. In a statement issued on Monday, the coalition said the Taliban attacked the coalition patrol with small arms fire and roadside bombs as it moved through a local bazaar in the province where there were civilians.
"Coalition forces engaged the enemy, pushed through the hostile area, and traveled to a nearby Afghan National Army checkpoint," the coalition said in a statement. "An investigation is currently underway to assess whether there are any civilian casualties as a result of insurgent fire."
AP writers Amir Shah and Thomas Wagner in Kabul contributed.