Police said the husband of Ranjeeta Sharma, 28, was believed to have flown to Fiji, where both came from, with their 4-year-old son Friday, the morning after her burning body was found by a passer-by on an isolated country road near Huntly.
They said her car had been found at Auckland airport.
Detective Senior Sergeant Nigel Keall told reporters that Interpol had been alerted to find the woman's husband, whom he did not name.
"He is considered a person of considerable significance to the investigation, and we are working with Interpol to locate and speak to him," he said.
"We are also working with overseas authorities to establish the wellbeing of the young boy and ensure his safety."
Police said earlier that a post mortem indicated the woman, who worked at Auckland's Middlemore Hospital, was still alive when she was set alight with an accelerant.
The Waikato Times newspaper said police would not comment on whether the case was a "bride burning", or honour killing, but quoted Roy Vellara, president of the Waikato Indian
Cultural Society, as saying the name Sharma was common in North India where most honour killings were performed.
Published 24 January 2011, 03:31 IST