Detectives working on the mysterious disappearance of John Beckenridge and his step-son have received tip-offs from the public that the pair might be hiding out in New Zealand.
Mr Beckenridge allegedly abducted Mike Zhao-Beckenridge, 11, from James Hargest College's junior school in Invercargill on March 13.
A week later, Mr Beckenridge's blue Volkswagen Touareg was found at the bottom of an 88m cliff near Curio Bay.
Their bodies have not been found.
Police are now treating it as a missing persons case.
Interpol is on high alert and some of Mr Beckenridge's friends believe he has faked their deaths and is hiding out in either New Zealand or abroad.
Over the past week, police have received calls from the public about possible sightings of the pair "across New Zealand".
However, each sighting has been ruled out by officers who checked out the leads, Southland area commander Inspector Kelvin Lloyd said.
"Police are continuing to assess the information we currently have and looking at what further enquiry can be made," he said.
"We continue to ask the public to assist with any information they may still have."
Police say they have not received "any confirmed information" that suggests Mr Beckenridge and the youngster have left the country or even the Catlins area.
Border alerts were flagged up within 24 hours of Mike's disappearance.
Aviation commentator Peter Clark says it would be "improbable but not impossible" to secretly flee New Zealand by helicopter.
Criminologist and ex-con Greg Newbold believes it is "definitely possible" to disappear, in New Zealand, or abroad, especially by sea.
Southland's harbourmasters office, which monitors all of the ports and harbours in the region, has not received any reports of missing vessels or irregular activity since March 13.
"We'd certainly know about it if there was," a spokesman said.
The region's harbourmaster had not been approached by police for any assistance with the case, the spokesman said.
Swedish-born Mr Beckenridge, 64, is an experienced commercial helicopter pilot who was also variously known as John Robert Lundh, Knut Goran Roland Lundh, and John Bradford.
Up until last September, he had been working as a full-time pilot for Pacific Helicopters PNG in Papua New Guinea Eastern Highlands province capital Goroka.
"We have given all of our information to [New Zealand] police," Pacific Helicopters PNG chief executive Mal Smith told NZME. News Service.
"We knew he had problems with his wife, and problems getting access to his kid, but we didn't know it was to that extreme."
Mr Lloyd said a range of police staff from different policing units are currently involved in the case.
He said that while police deal with complex missing person enquiries on a regular basis, officers involved in the Beckenridge case are "frustrated that we have not been able to give the family definitive answers".
Customs, which controls New Zealand's borders, refused to comment on the Beckenridge case, referring media enquiries to police.