However, Education Minister Alan Tudge says the religious discrimination bill will not allow a school to reject a teacher based on their sexuality or other trait.

The draft bill will be presented to a joint coalition partyroom meeting in Canberra on Tuesday and could be introduced to parliament as early as Wednesday.

It is understood a contentious part of the bill - known as the "Folau clause" - has been scrapped from an earlier version.

The section would have protected organisations from indirect discrimination claims if they acted against employees for misconduct for expressing their religion.

There had been a push from conservative groups for the bill to allow individuals and organisations the freedom to make statements of belief, such as Israel Folau's controversial social media posts saying homosexuals would go to hell.

Folau, who was sacked by Rugby Australia in 2019 over the posts, later received an apology from the body and a confidential settlement.

Also believed to be axed is a section in the bill allowing healthcare providers to "conscientiously object" to providing a service on religious grounds.

Mr Tudge told Sky News on Wednesday the bill would uphold the right of a religious school to employ teachers of their own faith.

"This is a critical principle at stake here ... you can't be a Catholic school if you can't employ Catholic teachers, you can't be a Muslim school without employing Muslim teachers."

Asked if it also meant a Catholic school could reject a gay teacher, Mr Tudge said: "That wouldn't be lawful under our bill."

But Equality Australia chief executive Anna Brown labelled his comments "breathtakingly misleading".

"Nothing in this religious discrimination bill acts to fulfil the federal government's previous commitment to protect LGBT students," she said.

"In fact, the Morrison government's bill licences more discrimination against all our communities, by overriding existing protections for women, people with disability, LGBTIQ+ people and even people of faith."

Mr Tudge said while there had not been a significant problem to be resolved by the bill, the laws would enable schools to "provide a good education consistent with the values which they articulate".

The bill was an election promise by the Liberal-National coalition but has sat in the too-hard basket since then as conservatives and moderates disagree on how far it should go.

Labor is awaiting the detail before determining its position.

Australian Associated Press