Laeticia Brouwer, 17, was fatally attacked by a shark on Monday while surfing in Western Australia (WA).
It was the third deadly attack in the state within 12 months.
Environment Minister Josh Frydenberg said Australia would think about culling sharks or introducing other measures, such as drum line traps.
“In light of the recent shark attack the Commonwealth would welcome any proposal to put human life first,” he said Mr Frydenberg.
“This could include the newest drum line technology, shark exclusion nets, culling or other measures which WA sees fit.”
However, the state government said it would not deploy drum lines following the attack in the town of Esperance.
“They don’t actually make our beaches any safer,” WA Fisheries Minister Dave Kelly said.
The fisheries department said it believed Ms Brouwer was attacked by a great white shark after examining photos of her damaged surfboard.
In 2014, the state trialled a shark cull on seven beaches using baited traps, but it proved controversial and was halted by an environmental regulator. More than 170 sharks were caught but none of them were great whites.
New shark nets have recently been installed at some beaches in the state.
Ms Brouwer’s uncle Steve Evans said relatives were “terribly heartbroken” by the tragedy.
“We take comfort in the fact that Laeticia died doing something that she loved,” he said.
“The ocean was her and her family’s passion. Surfing was something that she treasured doing with her dad and her sisters.
“Laeticia will be greatly missed by her family, friends and everyone who knew her.”
The beach will remain closed until further notice