GAY and lesbian rights activist Rodney Croome is hoping to convince Opposition Leader Will Hodgman to change his mind and offer Liberal MPs a conscience vote on legalising same-sex marriage.
Mr Croome said that he had sought a meeting with Mr Hodgman.
He said that some Liberal MPs were sympathetic to marriage equality and wanted a more thorough debate than was being allowed by their leader.
He would not name those members.
Mr Hodgman said that all members of the Liberal parliamentary team voted against same-sex marriage so there was no need for a conscience vote.
Mr Croome said that more people were likely to vote Liberal if the party allowed a conscience vote, based on recent national poll results.
``A national poll released (on Tuesday) by Galaxy research shows a net 20 per cent of non-Liberal voters, or almost 30,000 Tasmanians, would be more likely to vote Liberal if the party has a free vote on same-sex marriage,'' he said.
Mr Croome said that the Tasmanian Gay and Lesbian Rights Group would also launch a letter-writing campaign to convince the Liberals to offer a conscience vote.
``Liberals should support marriage equality because it will strengthen relationships and families, boost the Tasmanian economy and swing more voters their way,'' he said.
Premier Lara Giddings, who has offered Labor MPs a conscience vote, also questioned why Mr Hodgman was opposed to such a vote if all his members were against same-sex marriage.