Three members of a Korean-American family were among the victims killed during a mass shooting at an outlet mall in the U.S. state of Texas over the weekend.

According to the Dallas office of the South Korean consulate in Houston on Sunday, a couple in their 30s, identified by surnames Cho and Kang, along with their three-year-old child, died during Saturday's shooting at Allen Premium Outlets near Dallas.

The couple's other five-year-old child was seriously injured and is currently receiving medical treatment. The family, all U.S. citizens, reportedly resided in Dallas.

According to local media reports, a man immediately started firing gunshots at people at around 3:36 p.m. Saturday, local time, after stepping out of a vehicle in front of the outlet mall.

Eight people were killed, with at least seven others injured. The shooter was killed by a police officer who was in the area. 

Authorities have identified the man as 33-year-old Mauricio Garcia, with some reports suggesting he had links to far-right organizations.