A new poll commissioned by Australian Marriage Equality has reportedly shown that 72 per cent of Australians support legalising same-sex marriage.

The poll was carried out by the Liberal Party’s own pollster, Fairfax Media reports.

The Crosby Textor poll showed that 72 per cent of Australians supported legalising same-sex marriage and 77 per cent thought the Coalition MPs should be allowed a conscience vote on the issue.

The findings show an increase in support for marriage equality, up from 65 per cent in a Nielsen poll last August.

Such support extended across a range of demographics and age groups, the poll showed.

Liberal Democratic Senator David Leyonhjelm yesterday said he would introduce a private member’s bill to amend the marriage act, and called on Tony Abbott to approve a conscience vote.

His private bill, yet to be presented to parliament, will seek to remove references to "between a man and a woman" in the nation's marriage laws.

Marriage celebrants will be free to marry who they choose so they don't have to conduct ceremonies against their personal beliefs.

"Coming from the perspective of a relatively conservative, straight, middle-aged senator like me, whose vote is important to the government, I think the time is right," Senator Leyonhjelm told reporters in Canberra on Monday.

-With AAP