Two private members bills aimed at legalising gay marriage have been introduced into Federal Parliament.

Labor MP Stephen Jones signalled he would introduce a private members bill to legalise gay marriage at the ALP's conference in December.

But late last week Greens MP Adam Bandt and Tasmanian independent MP Andrew Wilkie indicated they would put forward another bill designed to achieve the same outcome.

Both bills were introduced into the House of Representatives today.

Earlier Mr Bandt said he believed Mr Jones' legislation would be voted on too soon and would end up being watered down, resulting in agreement on civil unions rather than gay marriage.

Mr Jones rejected the suggestion.

"I can categorically state that there will be no vote held in the House over the next couple of months," he said on Sunday.

"What we're doing tomorrow is merely the introduction of the bill, it won't go to the second reading or the debate stage for I'd expect quite some time yet.

"Any anticipation that there's going to be an early vote on this is really putting the cart before the horse."

Mr Jones said rumours the Coalition and Labor were working behind the scenes to get an agreement on civil unions are untrue.

"I think our focus should be looking at maximising the number of votes on the Labor side of the House, the crossbenches and the Coalition benches because we know that there are supporters in each of those three groups," he said.

Three bids before Parliament

With a Greens bill already in the Senate, there are now three separate bids before Parliament to change the Marriage Act, and not enough votes for any of them to succeed.

Coalition MPs do not require an explicit conscience vote to cross the floor, but the Opposition Leader Tony Abbott and frontbenchers like Joe Hockey have made it clear what is expected from the backbench.

"Our position is clear. We believe that a marriage is between a man and a woman and that's the way the Coalition will be voting," Mr Hockey said.

That is not deterring lobby groups like Australian Marriage Equality and its national convenor, Alex Greenwich.

"They are engaging in this issue more than they have before," he said.

"They are sharing what their concerns are with us about it, and they are giving us an opportunity to alleviate those concerns.

"Support within the Coalition is clearly growing."

Mr Greenwich said he would like to see all three bills considered by a Senate inquiry, set up last week, so it can decide which should proceed to a vote.

"I think all the bills that are being presented will have good parts and will have parts which will need to be amended," he said.

"And I think that that will be the subject of a process that will ensure the best possible bill goes to the Parliament."

The inquiry is not due to report until May, and a vote on any of the three bills is not expected before then.