The Green Party has rebuffed any suggestion it abstain on confidence and supply this term after Prime Minister John Key signalled that he could start to ask the Greens for more in return for some policy concessions.

The party's co-leaders, Russel Norman and Metiria Turei, met Mr Key and his deputy, Bill English, yesterday to discuss a potential arrangement between the Greens and National.

The parties agreed to continue with the Memorandum of Understanding they set up in the last term, under which they work on individual policies, such as the home insulation scheme, the cycleway, the cleanup of toxic sites, regulation of natural health products and pest trapping on Department of Conservation land.

However, Mr Key used the meeting to send a message to the Greens that he could be looking for more in the long term in return for concessions.

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Before the meeting, he said he wanted to discuss the future the two parties had together, including the conditions under which the Greens might agree to abstain on confidence and supply votes under a National Government.

"If there is a broader relationship to be had, then I'm interested in having those discussions. So before we get anywhere near any kind of Memorandum of Understanding I want us to have that broader discussion."

Ms Turei said they had agreed there would not be an abstention agreement this term, but they would meet again to add to the Memorandum of Understanding early next year.

She said the Government already had a majority and did not need the Greens to abstain this term.

Although the Green Party had not shut the door completely on such a deal, she said she had made it clear which of National's policies were a barrier.

"We said during the election campaign that the issues that were important to us were not only kids, rivers and jobs, but also those things we wanted to stop, like state asset sales, welfare reforms and deep sea oil drilling. Both us and National know that."

She said the Green Party considered an abstention agreement, which allowed a government to govern, to be the same arena as a full confidence and supply agreement. "So, therefore it would be highly unlikely, although we didn't close the door.

"But in the circumstance of this Government, that doesn't exist."

Dr Norman said the exact projects which might be added to the understanding would be decided next year.

During the election campaign, the Green Party put its focus on policies that National might be able to consider, such as cleaning up rivers and creating "green" jobs to increase its chances of securing gains under National.

Another possible area of co-operation includes Catherine Delahunty's member's bill requiring employers to release information about pay rates broken down by gender to address inequity.