Senior members of the federal Liberal Party remain uncommitted to gender quotas after Scott Morrison suggested he was open to the idea.
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Health Minister Greg Hunt said he wanted at least 50 per cent of places in the coalition party room held by women.
Mr Hunt said the party "can and must do better".
"We've got more to do. Whatever way will get us there, I am open to."
But he is not prepared to say he supports introducing gender quotas, which the Liberal Party has long resisted.
"I support the outcome and I am very open as to the means," Mr Hunt told reporters in Canberra on Wednesday.
The minister said gender equity could be achieved through what he described as "active management" but if that failed, quotas could achieve the desired result.
"I am very open to that."
Some Liberals have expressed reservations about gender quotas but senior female frontbenchers have argued it was time they were introduced.
The Liberal Party has spent years pushing back against gender quotas, relying instead on non-binding targets.
Liberal senator Jane Hume is among many who will only say they are "open-minded" to gender quotas.
"I think it is worth discussing. But there is more to it than that. That's not the only solution," she told the ABC.
Senator Hume said quotas did work but they were a "top-down" approach.
"In a grassroots organisation like a political party, it is important to have that groundswell of support from the bottom-up as well ... which you need to shift culture at the same time as shifting the numbers," she said.
"When it comes together, that's when you hit your peak policy-making ability, that wisdom of crowds, the ability for more diverse voices around the table making for better decisions, policy and politics."
Senator Hume said role models, mentors and sponsors were also important in elevating women in politics.
She said succession planning in safe seats was an important tool at the disposal of political parties.
"These are really important cultural shifts and we have an opportunity now to have that conversation and take it the next step further, beyond simple quotas."
Nationals minister David Littleproud does not support gender quotas.
But Mr Littleproud believes women are more than capable of competing against coalition men, referencing an upset win over vanquished colleague Barry O'Sullivan.
"If you look at Susie McDonald, from Queensland. She won a pre-selection against a stale male and is now in the Senate," he told reporters in Canberra.
Australian Associated Press
