Mr Stewart said there had been some talk of offering a reward for information leading to police catching the kea killers - although a figure had not been decided.
"I am just following that up now," he told NZPA.
The killings were "senseless" and there were still no indications as to why somebody would kill the birds and so publicly dump them, Mr Stewart said.
Senior Constable Scott Carmody, of Arthur's Pass police, told NZPA police were following a "couple of lines of inquiry" over the killings.
Police had received a little bit of information from public, but was still seeking more.
There were some people police were eager to speak to, and there were some vehicles they were searching for, but were not willing to go public with descriptions just yet, Mr Carmody said.
He did not believe the culprits were "immediately local", but it was believed the Klondyke Corner and West Coast birds were connected -- they were killed within 24 hours of each other, and the spots were only an hour's drive apart.
Police also did not know why someone would want to shoot and dump and endangered bird.
"We can only imagine it's someone trying to make a point. But whoever has done it has failed to make a point; whether they have failed to point out what their point was or whether they don't have a point, we don't know."
Under the Wildlife Act, it is a criminal offence to kill kea. Offenders could face a $100,000 fine or six months in prison.
- NZPA
