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.
Federal Environment Minister Josh Frydenberg said he would consider new proposals including culling, but any action would rely upon the state government.
"In light of the recent shark attack the Commonwealth would welcome any proposal to put human life first," 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 has said it prefers the use of personal devices, known as shark shields, to culling or drum lines.
Any state government proposal would ultimately require federal approval.
WA's 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 drum lines, but it proved controversial and was halted by an environmental regulator. More than 170 sharks were caught but none of them was a great white.
New shark nets have recently been installed at some beaches in the state.
'Passion' for ocean
Ms Brouwer's uncle Steve Evans said relatives were "terribly heartbroken" by her death in the town of Esperance.
"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.
Australia will consider all proposals to stop shark attacks after the death of a teenage girl, the government says.