Ms Banks said that she would like to see the state become the first place to allow same-sex marriage.

Legislation allowing it will be voted on in the Legislative Council next week.

``The proposed (same-sex marriage) bill is a positive step towards the full marriage equality that we should  be seeking on a national scale,'' Ms Banks said.

``This is consistent with Australian anti-discrimination laws and consistent with our international human rights obligations.''

She said that it would not be the first time that states had driven progressive law reform only for the federation to follow.

Her office has not received any complaints based on a same-sex couple's inability to marry, but Ms Banks said that even if she did she would not have the authority to consider it.

The Examiner reported on Thursday that support for Tasmania's bid to become the first state to allow gay couples to legally marry was slipping in the upper house.

Meanwhile, the newly formed Save Marriage Coalition has taken out advertisements in Tasmania's three newspapers urging upper house members to reject the legislation to protect the ``bedrock institution''. 

Coalition spokesman Guy Barnett said that the coalition comprised more than 12 community and church groups and businesses. 

``For the sake of current and future generations we hope the Tasmanian Same-Sex Marriage Bill will be thrown out,'' Mr Barnett said. 

He would not name the members of the coalition.