Australia already has strict gun control laws, which heavily restricted civilian firearm ownership after a gunman killed 35 people in Tasmania in 1996.
Other proposed actions include limiting the number of firearms any one person can have, requiring Australian citizenship as a condition for obtaining a firearms license, and limiting open-ended firearms licensing and the types of guns that are legal.
At least 38 other people are being treated in hospitals. Among them is a man security forces.
"My son has always been brave. He helps people. He’s like that," his mother, Malakeh Hasan al Ahmed, told Australian Broadcasting Corp. through an interpreter.
The Associated Press contributed to this report.