A large crocodile has killed a man at a notorious crossing on the East Alligator River in northern Australia, police said Friday.

Official guidelines warn against trying to walk over Cahill's Crossing which has seen numerous attacks and was swollen by recent rains.

Despite danger signs, the 47-year-old from a remote community in the Northern Territory waded across behind two women on Thursday afternoon.

"The two females made it across, however the male was reported missing a short time later," police superintendent Warren Jackson said in a statement.

Authorities shot dead the 3.3-metre (11-foot) crocodile and recovered the man's body about two kilometres (1.2 miles) downstream near Kakadu National Park.

"Cahill's Crossing is notorious for crocodiles and to walk across it to me is just foolishness," duty superintendent Bob Harrison told the Australian Broadcasting Corporation.

"You are tempting fate, knowing the size of the crocodiles in that area."

Australia is home to freshwater and saltwater crocodiles with the more feared "salties" growing up to seven metres long.

Saltwater croc numbers have exploded since they were declared a protected species and a spate of recent attacks has reignited debate about controlling them.

Government estimates put the national population at around 100,000.

They only kill an average of two people each year, but several high-profile attacks, including a woman snatched in May during a late-night swim off a beach in Queensland state, have renewed calls for culls.