The Taliban quickly claimed responsibility for the crash, but the coalition said in a statement: "Taliban's claims are false."
The statement 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 low altitude right after takeoff.
Kaufman said "it's too early to speculate" on whether the crash was suspicious or accidental in nature.
"We are anxious to help and find out what occurred," Kaufman said.
Deborah Hersman, chair of the National Transportation Safety Board, said late Monday that United States has not begun investigating the crash.
"The Afghan government has to make some decisions," she said. The Afghan government through the Afghan Civil Aviation Authority has jurisdiction to investigate civilian crashes.
"We don't have a role unless they ask us," she said.
The NTSB has investigated crashes in Afghanistan in the past, she said.
"It is sad to lose those serving our country, including personnel without uniforms, who provide services to those in uniform," she said.