Brenton Tarrant, the man charged in relation to the Christchurch massacre, is Australian and had been living in Dunedin until his alleged killing spree at two mosques on Friday.
Ardern was asked by reporters whether the 28-year-old was likely to be deported to Australia.
"I don't want to go too far down that track while we're obviously in early stages. Charges have been laid, we can expect additional charges, he'll be appearing in the High Court on the 5th of April, so there's obviously a process that needs to be gone through here.
"But I can say I am seeking advice on what will happen thereafter."
Ardern earlier said there was no place in New Zealand for perpetrators of such acts of "extreme and unprecedented violence".
Ardern signs a national condolence book at Parliament. Photo / Getty Images
Asked whether Ardern was referring to deportation before a sentence was served or after, a spokesman said she was looking at the issue in its entirety and getting advice on all options.
Tarrant did not require a visa to enter New Zealand because as an Australian he was able to enter the country and live there without one.
Immigration New Zealand, which said it could not comment specifically on Tarrant, said Australians were subject to the same deportation liability as any other visitor.
Ardern would not say how long Tarrant had been in New Zealand but said he had visited "sporadically".
At present Tarrant is charged with one count of murder under the Crimes Act.
Ardern confirmed Tarrant will be prosecuted in New Zealand.
The Prime Minister also confirmed her office received his manifesto minutes before the attack on Friday.
