Federal Coalition MPs and senators are spending the evening in a party room meeting, debating whether to have a free vote on same-sex marriage.

A private members bill to legalise gay marriage will be formally introduced to Parliament on Monday, with support from both Labor and Liberal MPs.

It is the policy of both the Liberal and National parties to oppose same-sex marriage, but some in the Coalition want to be allowed to vote in favour of the bill.

The meeting started mid-afternoon and has stretched into the night as MPs and senators make their cases.

"We're having an open debate, a very forthright debate," Environment Minister Greg Hunt told the ABC's 7:30.

"[It's] exactly what people would want from their parliamentarians.

"Every member, every single member who seeks to speak has the opportunity to speak.

"That's something to be very proud of."

The bill is being co-sponsored by the Coalition's Warren Entsch and Labor's Terri Butler.

Labor allows its parliamentarians a conscience vote and have challenged the Coalition to do the same in the hope it will give the bill a chance of success.

Canberra Airport puts its support for marriage equality up in lights. ( Twitter: @CanberraAirport )

At an earlier Liberal party room meeting, Education Minister Christopher Pyne warned Prime Minister Tony Abbott he ran the risk of being seen to be "branch stacking", after the PM suggested the joint Coalition party room, not the Liberal party room, should decide whether MPs get a free vote.

It is understood Mr Abbott's suggestion that the whole Coalition party room should decide on the issue was met with audible gasps from gay marriage supporters who felt blindsided.

The decision being made by the joint party room would likely make it harder for a free vote to be granted, given so few Nationals support gay marriage.

Mr Hunt rejected suggestions it was a move designed to thwart those seeking a free vote.

"I'd say, very clearly, that prior to the election our position was that there would be a meeting of the Coalition party room," he said.

"When [the issue] was raised today, [Tony Abbott] didn't delay or demur, he offered to proceed to a discussion today.

"I think that is very admirable."

A number of conservative politicians have told the ABC they are expecting the status quo to remain after the meeting.

Prominent campaigner against same-sex marriage Liberal Senator Cory Bernardi was confident there would not be enough support for change.

"It would be good to resolve this issue so we can return to matters of governance that are important to mainstream Australia," he said.

When asked whether he thought there was enough support for a free vote, he responded, "I never contemplate defeat so there is no chance".

Government MPs and senators who flew back into Canberra this week were greeted with a fresh pitch from advocates for same-sex marriage.

The managing director of the airport, Stephen Byron, allowed a rainbow light display to be installed across the gateway in support of allowing gay couples to wed.