Police in the eastern province of Kunar first said three children were killed in the incident on Monday but the interior ministry in Kabul later said only one had died.
Nato's International Security Assistance Force (ISAF) said the two wounded were seven-year-old girls. The dead child was also a young girl.
The girls were being treated at the main US base at Bagram, near the capital Kabul, a spokesman with the US-led coalition said.
The ISAF troops had been setting up mortars to fire into areas where they had previously come under attack, ISAF spokesman Major Luke Knittig said. The area in Pech district is a hotspot for attacks by Taliban.
In a test, one of a round of five mortars fell short of the target for technical reasons, Knittig said.
"We extend our sympathies and we are taking every effort to ensure children involved get the best care," he said.
An inquiry had been launched into the incident and an ISAF team had already been into the area to visit the families involved, he said.

Copyright AFP (Agence France-Presse), 2006