Attorney-General Mark Dreyfus last week flagged changes to the appointment process for the Australian Human Rights Commission to establish a merit-based selection approach.
The independent agency - tasked with protecting and promoting human rights in Australia and internationally - lost its 'A'-status accreditation in March due to questionable processes to appoint commissioners.
Greens MP Stephen Bates proposed an amendment to the government's proposal which would establish an LGBTQI commissioner, calling the lack of such a post an oversight that could be fixed by parliament.
"This would send a strong and clear message to the LGBTQIA+ community that the era of homophobia and transphobia from the previous government has come to an end," he told parliament on Tuesday.
"(It would) signal a new approach in engaging with and protecting communities that have suffered systemic oppression for centuries."
Independent MP Zali Steggall supported the proposal, reflecting on the debate about transgender women in sport started by her Liberal election challenger Katherine Deves.
"There was a huge amount of misinformation when it came to participation in sport of transgender women and ... there was a lack of leadership coming from the Human Rights Commission to establish clearly the true facts and where the law actually sits," she said.
"I do believe for many groups in our society it's important that there is a human rights commissioner taking care of their specific issues."
But Mr Dreyfus said the government's proposal was focused only on the selection and appointment process, not the roles of the commissioners themselves.
"The government recognises that it's important to consider how best the commission can operate to promote and protect the human rights of all members of the Australian community, including the LGBTQIA+ people," he said.
"This bill is not the vehicle to create such a position."
Instead, the government's bill is intended to establish transparency in the commission's appointment process and support its international re-accreditation, Mr Dreyfus said.