The private member's bill comes amid heated debate among government MPs about whether to change the law or put the matter to a plebiscite.
The government's official position is that marriage should only be between a man and a woman.
Prime Minister Tony Abbott has denied government MPs a free vote on any bill legalising same-sex marriage.
The bill allows couples, regardless of "sex, sexual orientation, gender identity or intersex status" to marry.
Australia's Marriage Act limits marriage to a union of a man and a woman.
The bill was introduced by government backbencher Warren Entsch, one of several government backbenchers who plan to defy Mr Abbott by crossing the floor of the parliament to vote in favour of marriage equality.
The ban on a free vote for government MPs means it is likely to fail.
Mr Abbott has said the matter should be "put to the people" in a non-binding plebiscite after the next general election, due in 2016.
Meanwhile, cross bench senators have backed an Australian Greens bill calling for a gay marriage plebiscite before the election.
In an impassioned speech, Mr Entsch spoke of how his bill, which has cross-party support, was designed to promote a more inclusive Australia.
"Being gay is not a lifestyle choice," the Queensland MP told the parliament.
"This bill does not create different classes of marriage," he said.
"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."

Poundland wants to buy its closest rival in an agreed deal worth Â£47.5m in cash and Â£7.5m in shares.
Initial investigations by the Competition and Markets Authority (CMA) said this could cause issues, including store closures, in 80 areas.
Now Poundland has rejected the CMA's suggestion to re-think the deal.
In its initial findings, the CMA said the deal could worsen the position for shoppers in local areas owing to a cut in quality, fewer promotions and store closures.
It said there was "a realistic prospect of substantial lessening of competition" in these areas where the two companies overlapped.
The authority suggested the concerns could be addressed in a "clear-cut manner" by the companies to prevent a full investigation.
Now Poundland has said there would be no changes to its plan, and has invited the CMA to move to a full review.
The company said it "remained confident that the combination of the two businesses will provide better choice, value and service for 99p Stores' customers".
It also claimed that the deal was "great" for anyone who held a stake in either business.

The annual June event - known as the Hoppings, after an old English word for dance - features more than 300 rides, sideshows, and other amusements.
The Discovery Museum exhibition explores the fair's history and the lives of the travelling showmen.
Visitors will also be able to play on vintage slot machines.
The gathering began as a Temperance Fair in 1882, in what was seen as an antidote to the Newcastle Races which had, up to then, been held on the Town Moor.
Through the years, generations of travelling families from all round the country have taken part in what is believed to be the largest such event in Europe, and it continues to attract tens of thousands of visitors.
The Discovery Museum exhibition - which runs until 1 October - features more than 50 vintage working amusement machines, from What the Butler Saw (early moving pictures) to pinball and fruit machines, which visitors can play using old pennies purchased from the museum.
Carolyn Ball, Museum Manager said: "The Hoppings is firmly placed in Tyneside's events calendar and has been loved by people in the area for generations.
"The exhibition will celebrate the history of the famous fair and visitors can step back in time and have a go on lots of rare vintage amusement machines."
A controversial bill to legalise same-sex marriage has been introduced to the Australian parliament.
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Discount store Poundland has invited the competition authorities to move to a full review of its proposed tie-up with rival 99p Stores.
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An exhibition celebrating the 135th anniversary of what is billed as the largest travelling funfair in Europe has opened in Newcastle.