Livingstone was described as 175 centimetres tall, Maori and of medium build.
It's thought he might have two suitcases with him.
He was on an extended supervision order, or ESO, which was an order for offenders who'd completed jail sentence and were considered to pose an ongoing risk of committing child sex offences. They were for offenders who legally could not be kept in prison any longer.
The sex offender left a suicide note before going on the run, police confirmed this morning.
Detective Inspector Grant Wormald also told Radio New Zealand there'd been potential sightings of the fugitive in Whangarei, Palmerston North, and Wellington but Livingstone remained at large.
Livingstone's victim had been told of his escape, Mr Wormald said.
Police were tracking down Livingstone's friends, associates, relatives and his past contacts, he said.
Parents and caregivers should be "particularly vigilant" around schools, Mr Wormald said.