Prime Minister Anthony Albanese flagged an easier pathway to citizenship and voting rights for Kiwis earlier in the year, pledging to have a proposed framework ready by early 2023.
In a meeting in Canberra on Friday, Senator Wong said a common sense approach was being taken to the relationship.
"We want to progress issues that affect the lives of those New Zealanders resident in Australia, in ways that recognise our deep friendship and that apply common sense outcomes," she said.
The New Zealand foreign minister said she was pleased with the conversations and that she would continue to advocate for New Zealanders.
The pair also discussed ongoing threats caused by climate change as well as security in the Asia-Pacific.
"We can work together to support Pacific partners in their aspirations on the existential challenge of climate change," Ms Mahuta said.
She reiterated the relationship between the two countries remained strong.
"We are closely aligned in our responses to regional and global challenges, and we share aspirations in common with fellow members of the Pacific Islands Forum closer to home," Ms Mahuta said.
They also discussed Russian President Vladimir Putin's illegal invasion of Ukraine and Iran's human rights violations in the wake of the deadly protests against its authoritarian regime.
The talks took place in Canberra following the first ministerial consultation between the pair in Wellington earlier this year.
Next year will mark a series of milestones for the trans-Tasman relationship including closer economic ties, the special travel arrangement and 80 years of diplomatic missions in Australia and New Zealand.
Ongoing deportations of New Zealand nationals who have lived the majority of their lives in Australia, have been a sticking point in the relationship.
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