"The more I thought about it,the more I thought it was really important that we give someone a good opportunity to launch into the next election and particularly at the moment,when it's so critical to hold this shocking government to account for their failure on fires."
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Senator Di Natale said he was not backing anyone to succeed him.
"It's a decision for the party room. There are 10 people;it's not a difficult decision when you only have 10 people."
Mr Bandt,the party's climate change spokesperson and only lower house MP,is expected to emerge as the frontrunner to replace Senator Di Natale. High-profile South Australian senator Sarah Hanson-Young has also previously nominated for leadership roles.
Senator Di Natale said he was leaving at a time when he had"never felt more supported by my party room".
"I feel like I'm leaving the party in good shape,at a time when it's my decision and no one else's."
Senator Di Natale also leaves as the party tries to resolve a years-long debate about whether it should allow members to elect the federal leader directly. After its national conference last November,the party set a May 2020 timeline to decide the issue,with Mr Bandt among those who say there is a"role for greater membership involvement".
Senator Di Natale,who was a GP and public health specialist before coming to Canberra,said he had been thinking about resigning since last year,but had given himself the summer break to confirm his decision.
He said he wanted to be able to support Ms Quarterman's career,after she had supported his for a decade,adding he had also been"knocked around"by knee surgery,to repair an old footy injury,last October.
"Having major surgery's good for your perspective,"he said.
"I'm sure there'll be a lot of people who are surprised with this decision. I was surprised when Bob[Brown] made his decision. And I was surprised when Christine[Milne] made her decision."
Senator Di Natale was hailed as a"new"type of Greens leader when he was elected almost five years ago. A Victorian,who did not come from the activist environment movement (unlike his Tasmanian predecessors),he was tipped to bring the party into the"mainstream".
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But,despite hopes of winning additional lower house seats in the 2019 election,the party came away empty handed. Senator Di Natale insisted he is proud of the overall result,noting all six senators up for re-election were returned. The Greens captured 10.4 per cent of lower house first preferences - the party's second best result,and a slight increase on 2016.
"If we just stand still,we'll elect three new senators at the next election,"he said.
Senator Di Natale listed medicinal cannabis legislation,Medicare-funded dental care and the since-dismantled carbon price scheme,as well as the Greens'campaigns for marriage equality and the banking and disability abuse royal commissions among his parliamentary highlights.
In December,he expressed deepfrustration about his party's "fractious" relationship with Labor,despite repeated overtures on his part for the two to co-operate on climate change policy. He is also angry and disappointed about the lack of climate action more broadly out of Canberra.
But he said he was leaving with a sense of optimism,due to growing local and global movements on climate change.
"We've endured this horrific bushfire season but there's no question there is a big movement building around climate change. A year ago,just to link the issue of bushfires and climate change was heresy and we were criticised[and] now it's accepted that there's a link."
His decision to resign is effective immediately,but Senator Di Natale will stay on in Parliament until a replacement is found for his Senate spot. This may take until the middle of the year,but he does not yet have clear plans about what he will do after that.
"I want to continue to be active in Greens politics,but I want to be able to do it in a way that allows me to be there for my family."
Over the Christmas break,after he had made his decision to quit politics,Senator Di Natale went camping with his family at Apollo Bay in south-western Victoria for a few days.
"Lucy and I both looked at each other and said,'We're going to be able to do a lot more of this now.'We both had a big smile on our faces."