"It's incumbent on every party president, every branch president, every person in the party around the country that we look to see how we can get more women into strong roles within our party," he told 6PR radio.
"We are, I think, under-represented here in our parliamentary ranks. But in terms of those who are here, we have a very strong representation in our party in the executive, in the ministry of the government."
His ministry includes six women, up from five under Malcolm Turnbull, but totalling a quarter of all ministers. Five more women are in junior positions.
Calls for gender equality in politics amid bullying and intimidation claims
Overall, less than a quarter of federal Liberal MPs are women compared to almost half of Labor representatives.
Former minister Craig Laundy has become the first male Liberal Party MP to come out in support of gender quotas.
Mr Laundy says he agrees with merit-based preselections, but fears that without a quota system the Liberals won't adequately increase female representation.
"Perhaps a first step is short-term intervention with a quota system in safe seats and selected safe Senate spots so the party can grow its female representation to the 50/50 level," he told The Australian.
South Australian Liberal MP Rowan Ramsey is also open to the suggestion.
"It is a bit of mystery why we don't have more women in the parliament. Maybe it's something about the workplace that is making them reluctant," Mr Ramsey told reporters in Canberra.
Liberal frontbencher Sussan Ley first raised the prospect of adopting gender quotas, with senior MPs including Marise Payne and Julie Bishop publicly lamenting the low number of women.
However, Liberal ministers including Simon Birmingham, Steve Ciobo and Josh Frydenberg are all satisfied with the party's target of 50 per cent female representation by 2025.
Liberal senator Eric Abetz concedes many women of great merit have been overlooked in the past.
"But quotas for the sake of quotas, all I say to you with respect is, have a look at the Labor party side of the parliament and you can see what quotas do and it ain't a good look," he said.
Meanwhile, Liberal senator Lucy Gichuhi appears to be backing away from threats to name bullies within the party.
The South Australian senator had threatened to use parliamentary privilege to publicly out colleagues accused of bullying and intimidation during last month's Liberal leadership crisis.
"Regarding bullying in my political career: Yesterday I had a discussion with Prime Minister Scott Morrison. The prime minister has taken up the issue," she posted to Twitter.