Late on Sunday, Rebecca Vassarotti was on track to pick up a second seat for the Greens in Kurrajong and Jo Clay was ahead for the fifth and final seat in Ginninderra.

Seats in Kurrajong and Murrumbidgee were retained and one was picked up in Yerrabi as the party heralded a 3.4 per cent swing in their favour.

Mr Rattenbury said he had a "quiet optimism" from the outset, coming off the back of the Greens' performance in the 2019 federal election.

"We knew from the start of the campaign if we could replicate that we could win a seat in every part of Canberra," he said.

Mr Rattenbury would not be drawn on whether the party had intentions to sit on the crossbench or push to hold ministerial positions including the role of deputy chief minister, saying those decisions would come after meeting with party members early this week.

"This has been a vote for the Greens and a vote for the ambitious agenda we took forward. This has not been a vote for just a Labor government, this is a vote for a two-party government," he said.

However, Chief Minister Andrew Barr shot down the prospect of Mr Rattenbury taking on the deputy role, and cast doubt on the notion multiple Greens members would play a part in his cabinet.

"I think it would be unlikely that any of the new Greens who have just been elected would immediately go into a ministerial position," Mr Barr said.

"We got nearly 40 per cent of the vote and we are going to be the single largest party in the chamber, so it is Labor's election commitments that we will be focusing on delivering. Where there is overlap, or where there is alignment with Greens policies .. we will have those discussions."

Mr Barr said "minor parties don't get to dictate to the Chief Minister which portfolios they have", and he would embark on a negotiations throughout the week.

"There won't be demand. It won't be shouty. It will be focused on our community and implementing the policies that we need to implement," he said.

Mr Rattenbury, who held a place in Mr Barr's last cabinet, said on Saturday night his party had struggled to make an impact on planning and housing policy, which became central to their 2020 campaign.

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He said it was too early to determine whether he would push to take on those portfolios.

"We are not satisfied with the way this city is developing," he said.

"We want to see more green space, we want to see buildings that are better built for the future climate that keep peoples cost of living down not through some short term sugar hit like the Liberal Party were offering but sustained long term better thinking about how we build this city."