Speaking to media this afternoon, Jacinda Ardern said there was "no evidence" to support some of the claims circulating around the case.
The government moved Northland from alert level 2 to alert level 3 in a sudden announcement last night, after an Auckland woman who had visited Northland tested positive for the coronavirus.
Speaking to multiple media outlets today, former deputy prime minister Winston Peters claimed the woman had gang connections and travelled through Auckland's border to the Bay of Islands and back.
He said there are more details that officials know and should have been made public.
But Ardern said there was "no evidence" to back up some of the claims that have been circulating online and the government was not withholding any vital information.
"As we've had information about their movements, we've released them. But this is a case where the individual, despite the involvement of the police, has not been forthcoming and that is why we took a very precautionary approach, and that was the right one.
"What we do know from video and CCTV footage is that the individual in question was travelling with a woman. We know that the place in which they were staying for that period of time has also confirmed that they were travelling with a woman. And the person that has been implicated through some of that social media chat, has themselves confirmed that they were not in the Northland region.
"My understanding is that police have identified that individual and is working hard to locate them."
She said the move to alert level 3 was necessary because "we have large gaps in what we know of their movements".
The woman initially returned a weak positive test for Covid-19 in Whangārei earlier this week and that was confirmed in Auckland on Thursday.
The woman remains in an Auckland quarantine facility.
Three new locations of interest in Te Tai Tokerau were added by the Ministry of Health today.
They are the Comfort Hotel Flames in the Whangārei suburb of Onerahi on Saturday 2 October from 6pm to 6.30pm; Pepe's Dairy in Onerahi on Sunday from 9am to 10am; and the Department of Conservation Uretiti campsite in Whangārei on Sunday, from 5pm to 6.30pm.
Last night contact tracers had only been able to identify two petrol stations in Whangārei.
Contact tracers have not yet been able to contact a second person, who is thought to have travelled with the woman.
Covid-19 Response Minister Chris Hipkins yesterday said police were needed to track down the infected woman, as she did not provide sufficient information to enable her to be contacted with the results of her second positive test.
She had not cooperated with contact tracers, he said.
Hipkins said the woman used false information to get travel documents and spent several days in Northland. When it was discovered and revoked the woman was already back in Auckland.
She has not given a reason for being in Northland, or details of another woman who is believed to have been travelling with her.
Hipkins is not ruling out dropping charges against the woman in a bid to cut a deal for her cooperation saying he would consider options which might encourage her to be more open with health officials.
