But Ardern rejected the suggestion that Labour and the Greens were "tied at the hip" by their MOU.
"We gave transparency to voters and told them that if you want both of us in government then we will deliver that coalition.
"It doesn't change the fact that we are an independent party."
Ardern said she commented publicly about Turei last week because she would face questions about the Green co-leader's suitability for Cabinet if the Labour leader became Prime Minister.
Beyond that, the controversy surrounding Turei was a matter for the Greens, she said.
She was "focused entirely on Labour".
Asked whether she had ruled out a ministerial portfolio outside Cabinet, Ardern said: "That's not something I'm focused on right now".
The two parties have been talking behind the scenes about the Greens' situation, including discussions between co-leader James Shaw and Labour's finance spokesman Grant Robertson.
Ardern admitted the talks were taking place, but she was not involved in them. Deputy leader Kelvin Davis said he "hadn't had a word" to the Greens.
The chaotic scenes within the Greens were not destabilising the left-wing bloc, Ardern insisted.
"I deliver stability. As leader of the Labour Party, I focus on the stability I deliver as leader of our party."
Turei has been under pressure since admitting three weeks ago to historical offending while on the benefit. She said on Friday she would not resign, but she would not seek a ministerial role if in government.
Ardern supported that move, saying she would not have allowed Turei to be in her Cabinet.