Police have made the “gruesome” discovery of human remains in a river bed after a 12-year-old girl went missing in a suspected crocodile attack.

Northern Territory Police confirmed the remains found near Palumpa, about 360 kilometres south-west of Darwin, were believed to be that of the child.

Her family reported there was a “black” crocodile in the area when she went missing while swimming in Mango Creek on country on Tuesday.

The discovery followed an extensive search to try to find the girl.

“It was particularly gruesome. And a sad devastating outcome,” Senior Sergeant Erica Gibson said on ABC TV.

“For the family, it is the most devastating outcome possible for them. They are in a state of extreme shock. And disbelief.”

Gibson said the difficult search took about 36 hours and it was believed a crocodile was responsible.

“At this stage we believe that a crocodile was involved,” she said.

“The trapping of crocodiles in that waterway will continue.

“Police members, including search and rescue, are currently working with local rangers, crocodile traps have been placed in that waterway.

“Those activities involving the capture of crocodiles will continue.”

Gibson commended the actions of everyone involved.

“They were diligent and work relentlessly,” she said.

“It’s not the outcome we were hoping for but for the family at least there is some small element of closure.”

Previously, Gibson told ABC Darwin the family regularly visited their “homeland” for holidays.

“They had attended the area, as they do for their holidays on homelands,” she told the ABC on Wednesday afternoon.

“The children and other people from the family group were swimming and it was reported that the child was missing.

“It was reported that a black crocodile was seen in the immediate area.”

Police received reports of a missing 12-year-old about 5.30pm on Tuesday near the community of Palumpa.

Local police and community members began searching the area on Tuesday with a search and rescue team deployed.

-with AAP