Government MP Warren Entsch has delivered a passionate speech in favour of legalising same-sex marriage, predicting the nation will not be united until gay couples have equal rights.

The moderate LNP backbencher has become the first Coalition MP to introduce a bill to legalise same-sex marriage, despite knowing it is highly unlikely to go to a vote before the next election.

"The main purpose of this bill is not a complex one," Mr Entsch told Parliament.

"It is to give same-sex couples in Australia the same right to marry the person they love as that which is currently only granted by law to heterosexual couples.

"This bill is designed to promote an inclusive Australia, not a divided one.

"A divided nation is what we will be if we continue to allow discrimination in relation to marriage on the basis of a person's sexuality."

The private members bill is expected to be put on the backburner by the Government-dominated selection committee that decides which legislation goes to a vote.

Mr Entsch's plans to introduce the bill triggered close to six hours of Coalition debate last week to thrash out the party's position on a free vote.

Two-thirds of Government MPs and senators voted to keep the existing position against a conscience vote, effectively confirming a bill would be defeated if it went to the floor of Parliament.

Before delivering his speech on Monday, Mr Entsch embraced Labor co-sponsor Terri Butler and thanked her for providing support.

The bill was also backed by another Labor MP Laurie Ferguson, Government backbencher Teresa Gambaro, Greens MP Adam Bandt and crossbenchers Andrew Wilkie and Cathy McGowan.

"We live in a modern society where women and Indigenous people have equal rights to vote, mixed-race marriages are acceptable and being gay is something not to be ashamed of," Mr Entsch said.

"The institution of marriage is about two people making a commitment to a relationship for life.

"Who is to say that one person's love for another person is in some way lesser because of their gender make-up?"

Mr Entsch referred to his own experience as a young man in rural Queensland, saying he was "enlightened" when a male friend transitioned to become a woman.

"Her courage in taking this step in the 1970s left a lasting impression on me while highlighting the futility of the nature versus nurture argument."

Referendum vs plebiscite: PM promises plan for popular vote will be finalised soon

Prime Minister Tony Abbott has promised a popular vote on same-sex marriage after the next election, but is under increasing pressure to detail how the ballot would take place.

The Cabinet meeting will be overshadowed by deep division over whether to hold a referendum to change the constitution or an opinion poll style national plebiscite.

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"We're not going to dwell on this and we're not going to drag out the process," Mr Abbott said.

"Very shortly we will finalise the precise process for going forward.

"It will be a people's decision and it will be in the next term of parliament."

Communications Minister Malcolm Turnbull has been calling for the process to be sped up, and a national plebiscite to be held before the next election.

In his speech Mr Entsch urged his colleagues to make inroads towards a resolution by the end of the year.

"I think it is very critical for us as the issue progresses in the coming months," he said.

"We need to aim for a very, very high standard of dialogue and I think we need to deal with this issue with the respect, the patience and the dignity that it does deserve."

Abbott questioned over no-show in Parliament

Labor has questioned why Mr Abbott decided to hold a media event away from Federal Parliament at the same time as Mr Entsch was delivering his speech and introducing the bill.

Ahead of the speech, Labor MP Terri Butler said she was "disappointed he [Mr Abbott] won't even be in the building when the bill is introduced."

"Tony Abbott seems to be going out of his way to insult LGBTI people and their families," she said.

Mr Abbott held the event at an Australian Federal Police training facility and focused on abuse of the drug ice, describing it as an Australia-wide issue that required "national leadership".

"My priority is jobs, growth and community safety," Mr Abbott said.

"I absolutely respect the rights of members of parliament to bring private members bills forward."

Mr Turnbull and Christopher Pyne were the only Government frontbenchers in the Lower House for Mr Entsch's speech.