There have been no reported sightings of the pair being overseas, Mr Lloyd said.
Mr Beckenridge allegedly abducted Mike 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.
Mr Beckenridge's friends from Queenstown, where he lived, believe he has faked their deaths and is hiding out in either New Zealand or abroad.
Interpol is on high alert.
"Police have been in liaison with the Interpol office in Wellington since the beginning of the investigation," Mr Lloyd.
However, given that inquiries are ongoing, Mr Lloyd refused to say exactly which authorities police have been liaising with.
Police said they had not received "any confirmed information" that suggested Mr Beckenridge and the youngster had left the country or even the Catlins area.
Border alerts were flagged up within 24 hours of Mike's disappearance.
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.
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.
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.