Two victims shot dead at a high school ice hockey game in Rhode Island have been identified as the suspect's ex-wife and son, police said on Tuesday.

Robert Dorgan - who police said also went by the names Roberta Esposito and Roberta Dorgan - was found dead inside the Dennis M Lynch Arena in Pawtucket on Monday, apparently from a self-inflicted gunshot wound after what authorities said was a targeted attack.

Dorgan's ex-wife, Rhonda Dorgan, and adult son, Aidan Dorgan, died. Rhonda's mother and father along with a family friend were injured. All three were in a critical condition at hospital.

Police have not given a motive, but said it appeared to be a family dispute.

Video of the incident showed shots fired while players were on the rink, sparking panic as the teams scrambled to leave the arena, which is located a few miles from the state capital of Providence.