The Greens hold the seats of Melbourne and Brisbane, Griffith and Ryan in inner Brisbane.
The party had been hoping to build their representation to nine and play a key role in minority government, targeting Macnamara and Wills in Melbourne, Richmond in northern NSW, Sturt in Adelaide and Perth.
However early results put a quick end to that plan and showed some incumbents were in trouble.
Griffith MP Max Chandler-Mather was trailing Labor’s Renee Coffey by 61 votes, with the party suffering a 17.3 per cent swing against it.
Meanwhile, Brisbane MP Stephen Bates is expected to lose the seat to the Labor’s Madonna Jarrett.
With about 29 per cent of the vote counted just after 7pm WST, the Greens primary vote was 13.4 per cent.
However, the party remains hopeful of winning Richmond from Labor, where challenger Mandy Nolan had secured 33.7 per cent of the primary vote.
Prime Minister Anthony Albanese had repeatedly refused to negotiate any deal with the Greens, such as the one that Julia Gillard signed with Bob Brown to secure a minority Labor government in 2010.
“One thing will be crystal clear: the Greens will play a big role in the next parliament, and we’re the ones pushing for the real lasting reforms,” Mr Bandt said earlier in the day.
“We would like to see dental into Medicare for everyone, but we need to take action on the housing crisis and the climate and environment crisis well.
“We put forward ideas that we think could get done this year.”
Mr Bandt said he had expected the Greens to do well in counting.
“I know Peter Dutton’s only potential pathway to power runs through those seats in Brisbane,” Mr Bandt told Sky News on Saturday evening.
“We’ve been really clear that keeping Brisbane Green is key to keeping Peter Dutton out.
“We began our campaign up to with that message.”
Mr Bandt also said he had been getting “very positive feedback” on Perth candidate Sophie Greer, who is challenging incumbent Labor MP Patrick Gorman.
The Greens’ election platform also includes taxing billionaires and big corporations, prioritising fully funding health services so people can see the GP for free, wiping all student debt and ending unlimited rent increases.