"There are a large number of people we want to speak to.
"It may be some days before we reach out to everyone who is relevant to our inquiry."
Mr Clements stressed that just because police were speaking to certain people, it did not make them a suspect.
Dr Pat Tuohy, the Ministry of Health's chief advisor for child and youth health, said information suggested the level of anxiety from parents and caregivers was "reducing".
"The message that infant formula in New Zealand is as safe today as it was before the threat was made seems to be getting through to parents and caregivers.
"The Healthline reports about questions of children has halved overnight."
Mr Tuohy said Plunketline received no calls last night.
If children did become unwell, it was likely it would be a "serious medical condition" which could be treated with medical attention.
"The probability that anyone is going to be poisoned with 1080 is remote," he said.
Mr Clements would not comment on who police were interviewing as part of their investigation, or how they were conducting their investigation.
"I won't talk about police techniques, but the obvious and logical one is to simply speak to people.
"We are getting positive feedback from those we are approaching."
He said there was a "vast" number of people to speak to.
He also would not comment on whether police had received any forensic evidence from the letter the threat was sent in.
Mr Clements said police were working to identify all potential sources with regards to accessing 1080.
Environmental Protection Authority chief executive Rob Furlong said there were tight controls that limited who could access 1080.
In order to purchase 1080 legally, an individual was required to be an approved handler and have a controlled substance licence, he said.
All people purchasing 1080 had to be over the age of 17 and had to undergo a police check.
