The major parties cannot ignore any longer the discrimination against same-sex couples being allowed to marry the one they love, according to Greens Senator Sarah Hanson-Young.

Senator Hanson-Young, Greens spokesperson on Sexuality and Gender Identity, says the recent Federal election campaign has shown the community has already recognised that Australia's marriage laws are unfair and that change is necessary.

"We know that 60 per cent of Australians support marriage equality, they understand the effect of the current laws and how those laws deny same-sex couples a very basic human right,'' Senator Hanson-Young said.

"As we enter a new Parliament, it is time for the Government and the Coalition to take note of the increasing levels of public concern and act accordingly.

"Australia is lagging behind a rising number of countries who have already legislated to get rid of this discrimination, in many cases overcoming historic and religious opposition to the principle of marriage equality. If those countries can change their approach, then so can Australia.

"Our leaders may well have firm views on this issue, as is their right. What's important is that they extend the right to speak freely and vote honestly on marriage equality to all their members and Senators.''

Later today Senator Hanson-Young will formally re-introduce her Marriage Equality Bill into the Senate. The bill will sit on the notice paper while a commitment to a conscience vote in both houses is agreed to.

"We call on members of the public to contact their local MPs and Senators to emphasise the importance of this issue to the community and to urge a conscience vote ,'' Senator Hanson-Young said.

"It is only with the help of the community, with pressure being brought to bear from inside and outside Parliament, that we will secure a free and fair vote on marriage equality. It's time to end this discrimination, and today marks the next step in the campaign to achieve this goal.''