A sexually-motivated night-time burglar remains on the run from police in Wellington.

Police are linking an indecent assault and two burglaries on February 9, and a burglary on February 24. They're hoping a distinctive cap will help them track the offender.

Descriptions from the incidents, which were all in the Kilbirnie area, were very similar, Detective Constable Miriam Reddington said.

The burglar was described as a Maori or Pacific Islander in his mid teens to early 20s. He was clean shaven of medium build with dark brown hair.

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Police found a purple and yellow LA Lakers cap at one of the homes targeted, Ms Reddington said.

"We believe these incidents are sexually motivated and urgently want to hear from anyone with any information to prevent any further, more serious offending from occurring.''