The two Sydney men say they were married overseas earlier this year, however the Australian Tax Office (ATO) will not recognise the union.
Australian Marriage Equality (AME) said the situation was unfair and the group backed the couple in their fight against the ATO.
"Same-sex couples should receive the same treatment as opposite-sex couples", said AME national convener, Sharon Dane.
"This couple are simply standing up for their rights as Australian citizens and I commend them for this."
Ms Dane said the couple had tried to lodge their tax return online earlier this year, but it had been rejected.
The couple said that in previous years they were permitted to lodge a return indicating their spouse was of the same sex.
However, this year they received a letter from the ATO saying the Income Tax Assessment Act 1997 did not recognise their marriage and that they were not entitled to show each other as spouse on their returns.
Ms Dane said it was discrimination.
"The demand for marriage equality is not going to disappear but will continue to grow," Ms Dane said.
"It's time our politicians just dealt with the matter once and for all."
Prime Minister John Howard is currently reassessing legal discrimination against homosexuals as the ACT government pushes ahead with plans to make same-sex unions legal in the territory.
Comment is being sought from the ATO.