Prime Minister Julia Gillard says she will not allow Labor Party members to have a conscience vote on same-sex marriage.

The Greens plan to introduce legislation to amend the Marriage Act to allow gay and lesbian couples to marry.

The Greens are calling for a conscience vote on the issue, but Ms Gillard says that will not be necessary.

"The Labor Party's got a clear position about the Marriage Act," she said.

"So you should expect to see the Labor Party voting as a political party, voting in unison, if that position comes to Parliament."

Greens Senator Sarah Hanson-Young says the Prime Minister will face pressure from both inside and outside the Labor Party if she does not allow the conscience vote.

"It's very clear that the community is much further ahead on this issue than either Julia Gillard or Tony Abbott," she said.

"They're going to have to start justifying their outdated view, their view to keep discrimination to a group within the community that is growing louder and stronger and bigger."