An Australian girl was killed when Pakistani police mistakenly opened fire during a robbery response, prompting Canberra to demand a full investigation.

Police shot and killed an Australian child in eastern Pakistan, authorities said, with Canberra calling on Monday for an investigation into the incident that also wounded two of the girl’s family members. Police in Pakistan’s most populous eastern province, Punjab, said that officers responding to a robbery exchanged fire with the suspects who were holding the passengers of a family’s car at gunpoint on Wednesday. “In the ensuing chaos, the officer involved mistakenly assessed that the suspects....