He said the two parties needed to "get past the Punch and Judy show of politics" and work together on an ambitious national target for reducing emissions ahead of crucial climate talks in Paris in December. He challenged Mr Key to sit down with him to discuss the issue.
Through a spokesman, Mr Key said consultation on climate change included listening to the views of other parties.
The Prime Minister said last week that he was looking forward to facing Mr Shaw in Parliament - an approach which Mr Shaw said was part of a strategy by National to undermine him.
Mr Shaw's first parliamentary appearance as co-leader will be taking on Mr Key at Question Time tomorrow, and he said the Prime Minister should be "careful what he wishes for".
Mr Shaw's speech also gave an outline of the party's future direction.
The new co-leader said the Greens would not drop their social policies to focus more narrowly on the environment, because the two areas were inextricably bound together.
But he did promise some changes, saying it was his job to make the Greens "more like modern New Zealand". This would involve increasing Maori, Pacific and Asian membership and recruiting more farmers and businesspeople. "People vote for people they feel a connection to. If we aim to govern the country then we need to represent it," he said.
He wanted to double the party's membership of 6000 in the next year and double it again the following year.
His speech did not mention his party's most likely ally, Labour, once, though Mr Shaw has spoken of working with Labour and said the two parties polled best when they presented a united front.
HOW THE GREENS VOTED
James Shaw: 69 votes (54%)
Kevin Hague: 56 votes (44%)
Gareth Hughes: 1 vote (1%)
Vernon Tava: 1 vote (1%)
(Note: Mr Shaw won on the first round of preferential voting. Delegates cast votes on behalf of their electorate.)