The architect of the scheme, Labor's Jenny Macklin, said there was "clearly some scope to improve awareness" of it.

A University of Queensland review conducted two years ago found there was a lack of awareness of the scheme, despite a cultural shift for fathers to be more involved in their children's care. The review found men used their annual leave to add to their time off, which didn't leave much flexibility in later months if they were needed at home.

To be eligible for the dad and partner pay scheme, a person must be the biological father of the child, the partner of the child's birth mother, or an adoptive parent of the child.

Of 170,501 people who applied for the paid parental leave scheme, which offers the primary carer up to 18 weeks' pay at the minimum wage, just 620 were men.

Richard Fletcher, associate professor with the Faculty of Health and Medicine Family Action Centre at the University of Newcastle, said there was a lot more that could be done.

"One key problem is the fact that [the parental leave policy] is focused on a single carer looking after a baby," he said. "The idea is one adult is needed to look after a baby, and so if the mother is not working then the father must be. [The] idea is that sharing leave is based on the notion that if the dad is going to stop work and be involved in the baby, then the mother has to go back to work herself."

Dr Fletcher said Australia's policy encouraged fathers and partners to go back to work almost immediately, and the government needed to "both do more and do it differently".

"They need to do a lot more to support families who are having a baby, to avoid the ongoing costs of things like depression and children's difficulties, which cost the whole community a lot of money," he said.

"They need to do more in making that a more supported transition, so the father should have greater access to leave at the same time as the mother. The father should also have, as happens in other countries, encouragement to go to ante-natal appointments. [This will] encourage him to be part of the process, so it isn't him arriving on the day of birth in his role as the father, totally unprepared and without any connection to what is going on."