The "manifesto" was released by the accused gunman on March 15, just before the mass shootings at two mosques in Christchurch which killed 51 people.
According to the New Zealand Herald, neo-Nazis have been selling printed versions of the 87-page, hate-filled document from a Ukrainian encrypted instant messaging site for $4.
Ardern described it as "abhorrent and disgusting", but said New Zealand had little control over the matter. She, however, added that she would have no problem contacting Ukraine.
"I would no hesitation asking the Ministry of Foreign Affairs to make that kind of contact," she told reporters in Porirua.
The acting head of the Islamic Women's Council, Anjum Rahman, told Radio NZ she wanted the government to approach Ukrainian authorities to find those involved.
New Zealand's Chief Censor classified the manifesto as objectionable, meaning anyone found to be distributing it in this country could face up to 14 years in prison, or a $10,000 fine.
But that didn't mean the document was banned overseas, Ardern told media on Wednesday.
But she defended the Christchurch Call, a voluntary international agreement to stop violent extremism and terrorist content from spreading online.
"I don't think we should assume that just because an act doesn't fix everything that it's not worthwhile. The Christchurch Call will make a considerable difference," she said.
( With inputs from IANS )