"We can't as a nation deal with this on our own and that's why the work around the Christchurch Call and any other work around international agreements is so important," she said.
On Thursday, Ardern said 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.
"It's abhorrent but we only have the ability to control what occurs within our jurisdiction. But I would have no hesitation sharing New Zealand's view with the Ukraine."
New Zealand's Chief Censor has 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.
The channel selling the translated manifesto contains vile white supremacist messages and its administrator says he is trying to disseminate the text as far as possible.
Meanwhile, Corrections has been in damage control since it was revealed last week that an inappropriate letter from the 28-year-old Australian arrested over the Christchurch mosque shootings had been posted online after being released to a far-right contact in Russia.
Corrections boss Christine Stevenson has apologised and promised changes to the way mail is handled in jails. It was later revealed a second troubling letter from the alleged shooter had made it out, along with messages from a second white supremacist.
The Government is now mulling the laws governing prison mail.
