The Green Party is preparing for talks with Labour over what it hopes will be a formal coalition, saying that voters have clearly indicated that they want a more progressive government.
Shaw said he and co-leader Marama Davidson expected to have a conversation today with Labour leader Jacinda Ardern about when and what sort of negotiations would take place.
The Greens secured a return to Parliament with 7.6 per cent of the party vote last night, but Labour's strong result of 49.1 per cent meant it did not need the Greens to form a government.
Shaw said this morning he was not certain that Greens would be asked to form a coalition, but he was hoping for it.
He listed several reasons for why Labour should include Greens at the governing table.
"Progressive voters wanted a Labour-Green government," he told the Herald.
"We know that some of the people who voted for us were people that would otherwise have voted for Labour, but want the Greens to be part of the next Government.
"And a lot of people have voted Labour but have said 'Look I really want [the Greens] in there'. And I actually want a multi-party government, it's healthy."
Shaw said Labour would also be thinking ahead to the 2023 election and the need to keep potential support parties onside.
"And also, frankly, they'll want as large a majority in the House as they can, because it affects things like membership to select committees.
"So I think there's a lot of good reasons to be a part of it. But ultimately that will come down to the conversations we have over coming weeks."
The top priority for the Greens was advancing its policies, rather than being in coalition or getting ministerial positions.
"It's not about the jobs or the job titles, it's about getting the work done. And then the jobs flow from there."
Labour has already ruled out the Green Party's proposed wealth tax. Shaw was asked whether his party would push for different tax proposals or measures which it had not campaigned on to address wealth inequality.
"I would start with a question [to Ardern]," Shaw said. "You've ruled out a capital gains tax and a wealth tax, and you know there's a problem. What's your plan?"
If Labour wanted the Greens in government - either in a formal coalition or in a confidence and supply agreement - the final decision would be left to Green Party members.
Under last night's result, the Green caucus would expand from 8 MPs to 10 MPs. The new faces would be Teanau Tuiono, Dr Elizabeth Kerekere, and Ricardo Menendez-March. Special votes could bring in one more MP, Steve Abel.
Shaw was still on a high from last night's result, saying it far exceeded their expectations of between 6 and 6.5 per cent.
"I am stoked. Totally stoked. It was a banger, an absolute banger."
He also paid tribute to Chloe Swarbrick, who won the Auckland Central seat in a sensational upset. It was just the second electorate seat victory in Green Party history, and the first for any minor party which did not have a major party endorsement.
"It is phenomenal," Shaw said. "It really is testament to her as a remarkable woman and politician."
Asked how he would celebrate, he said he would get some sleep.
"That's quite a treat. We had quite a big night last night."