Bill Shorten has offered to withdraw his marriage equality bill if the Liberal Party introduces its own.
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The Opposition Leader made the comments in front of hundreds of people holding signs saying "Love is love" and "#FreeVote" on Victoria's Parliament House steps on Saturday.
The rally was held to call on the federal government to grant a free vote on marriage equality.
"What I offer Tony Abbott and the Liberals today is that if you don't like that it's the Labor people who are moving and seconding this law, we will relinquish our moving and seconding rights," Mr Shorten said to cheers.
"If you want to have your name on the piece of paper, we're happy with that. We just want everybody else to be able to put their name on a piece of paper too."
Mr Shorten said marriage equality was long overdue in Australia. "I know there is a lot going on, but the Australian people are smart, we can do more than one thing at a time."
Labor Senator Penny Wong called the movement towards marriage equality "unstoppable".
"We are here because our community is ahead of our parliament and we have to do something about that," she said.
Senator Wong said it was time the Liberal and National parties "support equality".
"I acknowledge the courage of those who have come forward and it is time for Tony Abbott to get out of the way."
Chris Jansen, who grew up in country Victoria, attended the rally with his partner Ryan Goodfellow.
"For us, we're not necessarily planning on getting married but it's more so the discriminatory factor," he said.
"For me, growing up in Mildura, any form of restriction on same-sex relationships has a negative connotation [and a] feeling of not being in the community."
Mr Jansen said homophobia had stopped him from coming out in Mildura and it was important the town's young people didn't go through the same experience today.
Mr Goodfellow said he had earlier thought of marriage as a religious construct but now believed that it was important to recognise everybody's rights.
"So the 15-year-old in high school today can stand up and be proud and be part of an inclusive Australia," he said.
Susan McCarthy said she came to the rally because she believed her lesbian daughter should have the right to marry.
"She really believes she should be able to get married when she meets the person she wants to marry, and I think she should be able to as well," she said.
"Marriage is the accepted norm and the major commitment people make to each other in a relationship and should be available to all people who are committed."
Mr Shorten's private members bill proposes replacing the words "man and woman" with the term "two people" to define who can be legally married.
Marriage equality campaigners estimate that if Liberal MPs have a free vote on the issue, same-sex marriage legislation would almost have a majority in both houses.
Human Rights Commissioner Tim Wilson, Victorian Minister for Equality Martin Foley and state shadow minister for equality David Davis were among the other speakers at the rally.
