As authorities searched for the missing 46-year-old woman off a beach in far north Queensland, independent MP Bob Katter urged authorities to take action against the animals.
Crocodile takes woman during night swim in Australia
Katter said crocodile numbers in northern Queensland state, where the predators have been protected since the 1970s, were "exploding".
"I've long called for crocodile culls in Far North Qld and believe crocodile hunting safaris could be a solution," he wrote on his Facebook page.
"Nature has a balance and the balance is completely out of whack. We can put nature back in balance if we have shooting safaris."
The issue raised its head after two women taking a dip in shallow water at Thornton Beach in the Daintree National Park on Sunday night were the victims of a suspected crocodile attack.
One woman felt something brush her leg and then saw her friend dragged away, reportedly crying out: "A croc's got me, a croc's got me!" The woman has not been seen since, despite an extensive search.
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Crocodiles are known to haunt the waterways of northern Queensland, and the area near Thornton Beach is a known habitat of the reptile, prompting much debate about the wisdom of a late-night swim.
Grahame Webb, who has worked in crocodile conservation for decades, said some waters were too dangerous to plunge into, no matter how inviting.
"When you're in a national park -- and dangerous animals are part of the attraction -- it just really is misadventure," he told AFP.
"People say, 'Let's just do it, it looks so nice' (but) you just don't swim in those sort of areas."
Crocodiles, he added, "can see perfectly well on a moonlit beach".
Saltwater crocodiles have become more common in northern Australia since they were declared a protected species in 1971. They are estimated to kill an average of two people each year.
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Several hundred are culled every year in the Northern Territory, neighbouring Queensland state, to protect the public and livestock.
But the Australian government knocked back the idea of trophy hunts in 2014, with Environment Minister Greg Hunt saying they risked "cruel and inhumane" behaviour.
Webb said there was a need for officials to be "horribly pragmatic" about crocodile management.
"You can't sugarcoat the management of crocs, you've just got to be horribly pragmatic. Crocodiles are the biggest killers of other crocodiles anyway."
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