A man is on the run after allegedly raping an elderly woman inside her home after sneaking in through the back door.

The woman, who is in her 80s, was at home in Woodroffe, outside Darwin, when the unknown man entered the property about 8.50pm on Wednesday. 

Police are yet to release a description of the suspect.

A spokesperson for NT Police said detectives are asking the public to come forward with any information or CCTV footage that could assist the investigation.

'Around 8:50pm, police received a report that a woman was sexually assaulted at her residence on Woodroffe Avenue, Palmerston,' the spokesperson said.

'An unknown male offender has allegedly entered through the rear door of the property, before sexually assaulting the woman and fleeing the scene.'

At a press conference on Friday morning, NT Attorney-General Marie-Clare Boothby said she was 'absolutely disgusted' by the attack.

'We need this person to be apprehended and dealt with because this kind of behaviour is not acceptable by our government,' she said.

Members of the public should contact police on 131 444 if they have information.