Australian police say they've found the remains of 12-year-old boy who was snatched by a crocodile while swimming in a water hole at Kakadu National Park on Sunday.

Michael White, the acting police commander in the Northern Territory incident, said search teams had come up with evidence that "strongly indicated" the boy had died in the attack, according to a report by the Australian Broadcasting Corporation.

The boy, whose name has not been released, was swimming with friends in a billabong, or water hole, when the crocodile attacked. Another 15-year-old boy was injured in the attack, suffering lacerations to both arms. The incident occurred in Magela Creek, which is near the town of Jabiru.

Students in the area were finishing summer break and approaching the start of a new school term. The boy would have returned to school Tuesday, the ABC reported.

A DNA test will be conducted to confirm that the remains found were the boy's, but based on the evidence available it seems clear the boy died.

"No specifics will be given in relation to the trauma or type of evidence located out of respect for the family," White said.

Rebecca Forrest, a spokeswoman for the Northern Territory police, told CNN that the boy's family has been informed.

"As expected they're grieving," Forrest said. "But the evidence is there that he's deceased."

A counselor and a Jabiru school principal are providing support to the staff, students and to the local indigenous families, a spokesperson for the area's department of education told the ABC.

According to police sergeant Stephen Constable, the crocodile first attacked the 15-year-old before turning on the younger boy.

"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," Constable said.

Crocodiles are common in Kakadu National Park, which is 171 km (106 miles) southeast of Darwin. As part of the search for the missing boy, rescue workers shot four crocodiles, three of which died, the ABC reported.

Visitors to Kakadu are urged to exercise caution when in the park, as crocodiles there have been responsible for a number of fatal attacks over the years. Scenes from the popular Crocodile Dundee movies were filmed at the park.

About a year ago a teenager had to fight off a 5-meter-long crocodile in the same location as Sunday's incident, according to ABC reporter Katherine Gregory.

"It's obviously a bit of a dangerous spot," she said, adding that locals and park visitors are regularly warned of the danger of crocodiles.

The summer wet season is underway in Australia at the moment, which Gregory reported is the most dangerous time to be swimming in creeks and water holes.