The two nations have been locked in a months-long stand-off, even though Australia has secured "overwhelming support" to bring COP31 Down Under.
Prime Minister Anthony Albanese wrote to Turkish President Tayyip Erdogan earlier in November in a bid to resolve the tussle.
The United Nations' annual Conference of the Parties lacks provisions to break deadlocks over such disputes, with the scenario relying on one side or the other voluntarily withdrawing.
However, Mr Bowen said Australia remained committed.
"We have the overwhelming support of the world to host" the 2026 conference, he told reporters at Sydney Airport on Saturday on his way to join this year's summit being held in the Amazonian city of Belem.
Australia wanted to co-host with Pacific island nations for the first time and demonstrate how to work together to fight the "existential threat" of climate change, he said.
"Our nation has a lot at stake when it comes to climate change but every effort we make now will help avert the worst impacts," he said.
"It's not a matter of fighting on for months afterwards - it gets decided at this conference.
"It's not a ballot process. That means we need to reach an agreement with Turkey - that's difficult."
Mr Bowen said he would continue to converse with Turkish counterparts during the week, while a regional diplomatic bloc of 18 countries, the Pacific Islands Forum, is backing Australia's bid.
Yet it has been overshadowed by domestic climate policy after the Liberal Party dropped its net-zero emissions target in a decision to be rubber-stamped on Sunday.
Opposition MP Leon Rebello maintains the party's choice was "driven by what's right for Australia", despite the majority of Australians believing the government should adhere to net zero by 2050 in some way.
"We don't support net zero by 2050 and the reason is ... because we have the licence to step away from it and put our own way forward," he told Sky News on Saturday.
With the United States absent from COP for the first time in three decades, China is stepping into the limelight as a leader in the fight against global warming.
Unlike previous years, when it had a modest pavilion with just a handful of seats available for mostly technical and academic panels, its display in Belem occupies prime space near the entrance next to host country Brazil.
China is also playing a more subtle role in filling the US void behind the scenes, with efforts to rally governments toward agreement.
