The state’s parliament changed its laws earlier this year to recognise same-sex marriages and civil unions from other states.
Greens leader Nick McKim said the party took the move because of federal government inaction on the issue.
"If there is no action from the Gillard government, then Tasmania is in a position to lead the way," he said on Tuesday.
"Nationally, pressure continues to grow for same-sex marriage to be recognised, and most Tasmanians would also share the opinion that all forms of discrimination should be removed from our institutions."
Australian Times analysis: Power to the independent on same-sex marriage.
But the laws are not likely to succeed without the full support of the Labor Party, who govern in minority with the Greens’ support.
Premier David Bartlett said it would be more appropriate for the changes to take place at a federal level.
"Anything less than amending the federal Marriage Act will not be equality," he told reporters in Hobart on Tuesday.
"I actually support, personally, equality for same-sex marriage, and at the next opportunity I will be going to the national ALP conference … and I will argue that case."
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