Police say Smith, who ahead of his life sentence had amassed a criminal history including convictions for blackmail, fraud, escaping custody, illegally having a firearm, the firebombing of a Greytown house and assault, could have had "outside help" to escape the country.
The alarm was raised on Sunday about Smith's non-appearance at an Auckland address.
A Wellington newspaper reported that while New Zealand has no extradition treaty with Chile, the United Kingdom does, meaning New Zealand may still be able to pursue him. Corrections national commissioner Jeremy Lightfoot said while Smith was declined parole, he was approved for overnight temporary release. Since March, he had completed five three-night temporary release stints.
In the 12 months before his March parole board hearing, he had successfully completed six one-day temporary release stints.
A relative of the man Smith murdered said it was "devastating" to realise he was on the run and told Radio New Zealand some members of her family had gone into police protection.
"My family is frightened, they're not in a good space at all. We just want him caught and this should never have happened, never," she said.
"I've spoken to one of my family who has been put in protection. They're extremely worried, this has upset their whole life yet again ... it's not right."
The woman said the family member who Smith had indecently assaulted was not in New Zealand anymore, but was told last night that Smith was on the run.
The circumstances of Smith obtaining the passport under the name Traynor and making arrangements to leave, and who may have assisted him, are central to the combined investigation, police say.