(CNN) -- Police have found evidence that "strongly indicates" a 12-year-old boy who was witnessed being snatched by a crocodile in a remote part of Australia was killed in the attack.
"No specifics will be given in relation to the trauma or type of evidence located out of respect for the family," acting police commander Michael White said in a statement Tuesday.
The family of the boy -- who would have returned to school Tuesday after the summer break -- have been informed, a spokeswoman for the Northern Territory police, Rebecca Forrest, told CNN.
"As expected they're grieving," Forrest said. "But the evidence is there that he's deceased."
As search crews continued to gather evidence Tuesday, shoot-to-kill orders remained in place for crocodiles longer than two meters around the small community where the attack occurred.
Three animals have been killed so far, ranging from 2.5 to 4.7 meters in length, Forrest said.
The boy had been swimming with four other children in a water hole near Mudginberri in the Northern Territory's Kakadu National Park on Sunday afternoon, when a saltwater crocodile attacked the group.
One of the boys, aged 15, was bitten by the animal but managed to escape. The crocodile then turned on his friend, aged 12, said police sergeant Stephen Constable.
"The 15-year-old boy was grabbed on his right arm. He started fighting off the croc, and it took him by the left arm; then it let him go and took hold of the 12-year-old boy, and swam off with him."
Police officers and park rangers have been using helicopters and boats to search the area since the attack occurred.
A crocodile expert who examined the first boy's wounds, believed the crocodile was between 2.5 to three meters long (around eight to nine feet), Constable said.
Search crews have also been looking for larger crocodiles that may have attacked the one that took the 12-year-old.
"On occasion a smaller crocodile may take some food, and a bigger crocodile will take it off them," said Constable.
According to local media reports, people had been warned against swimming in the area after a teenager survived an attack by a five-meter-long crocodile in the region in January last year.
Constable said this time of year is particularly dangerous due to seasonal flooding.
CNN's Pierre Meilhan contributed to this report.