ACL Managing Director Lyle Shelton said it was time for state parliaments to stop using parliamentary time to debate a federal issue.
"This is the ninth bill introduced by advocates seeking to redefine marriage in an Australian Parliament since 2010. They have used up much parliamentary time and the issue has had a fair go," he said.
"Marriage is a federal issue and the nation decided back in the 1960s to have uniform marriage law."
Mr Shelton said it was time to move on from the issue and urged same-sex marriage advocates to let state and federal parliaments focus on governing for the common good.
"It's time for parliamentarians to be given an opportunity to focus on things like the breakdown in child welfare with a stressed out-of-home care system or affordable housing for those at risk of homelessness," he said.
"Each time parliament spends time debating this issue is a lost opportunity to debate policies at the heart of government â health, welfare and economic stability," he said.
"It is time same-sex marriage advocates submit to the decisions of parliament rather than pursuing legislation by fatigue" he said.