Police believed Miss Boden and Veint were together, but did not believe she was being held against her will, he said.
Her father, Mark Boden, told the Otago Daily Times from his home in Adelaide, Australia, that he first heard of Miss Boden's disappearance from media reports.
He had a message for her: ''We just want you home safe, Lilly''.
Her friends also appealed to her on social media.
''Everything will be fine!! Please come home Lilly!!!!!'' one Facebook post read.
Another said ''please come home safely''.
Inspector Jensen said Miss Boden and Veint were friends.
It is understood she is also known to the alleged kidnapping victim, Mr Armstrong.
Police were still looking for Veint and Pita Wilson, 38, over the alleged kidnapping in the resort last week.
''This matter could be simply and quickly resolved if the pair got in contact with police, either directly or indirectly,'' he said.
''Although police have received some good information from members of the public, they are still keen to hear from anyone who may have seen Pita Wilson or Joshua Veint, or knows of their whereabouts.''
While neither man posed a risk to the public, they should not be approached, he said.
About 20 specialist staff, including a dog handler, were working on the investigation.
Aerial searches had not been conducted at this stage and police were keeping ''an open mind'' about the men's whereabouts - which could include the bush.
''We believe that Mr Wilson is in the Queenstown area and Joshua Veint ... we suspect that he's still within the greater Queenstown area.''
Police were staying in contact with Mr Armstrong, who was located just before midnight on Sunday.
Inspector Jensen would not comment on how long Mr Armstrong was allegedly held against his will.
The hunt for Veint and Wilson began on Friday, after an incident last Tuesday at a Queenstown address came to police attention.
Police would not reveal how the incident was revealed, other than it came to light during another police operation.
Insp Jensen is yet to elaborate on what that operation was.
Those involved in the incident were known to each other, he said.
Two men yesterday appeared in the Invercargill District Court in relation to the incident.
Anyone with information which may help police can contact Queenstown police on (03) 441-1600 or anonymously via Crimestoppers on 0800 555-111.
