He said the Green Party promoted Maori ownership of water - a policy which was separatist.
Turei's comment also drew fire from NZ First MP Tracey Martin on Twitter. Martin said that by describing her as racist "you make it very difficult to sit at the table and believe it is mutually respectful".
In response, Turei said she had respect for Martin personally "but persistent persecution of migrants by NZF is not ok. You can fix that if you choose".
It is a break in an apparent entente cordiale between the Green Party and NZ First and will concern Labour.
In 2005, Peters blocked the Green Party out of being part of a government with Labour.
Of late, although NZ First refused to be part of the agreement the Greens signed with the Labour Party, Peters has pulled back on his attacks on the Greens.
On Q+A, Turei said the Greens' relationship with Peters was "fine" and it was possible the Greens would have to work with NZ First despite concerns about its policies.
"My plea, I guess, to the New Zealand public is don't make that necessary.
"NZ First has not ruled us out, like they have done in the past and we have not ruled them out either. Because, actually, they may be necessary for the formation of a progressive government. I think this is just the political reality we have.
"Either it is going to be National and NZ First, which is completely unacceptable, or it may be the Greens and Labour with or without Winston."
The Green Party is launching its 2017 election campaign in Nelson today - an electorate it is targeting to try to oust National's Nick Smith.