Prime Minister Tony Abbott on Sunday ruled out Australia following Ireland's example and settling the issue by a popular vote, saying it was a matter for parliament to decide.
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Mr Abbott acknowledged the issue was important to millions of Australians, but said his immediate priority was boosting small business confidence through measures announced in the budget.
"This is obviously a serious issue, a very serious issue," Mr Abbott said.
"There are a range of views inside the Parliament; there are a range of views inside my party room; frankly there's a range of views inside my family.
"Inside the Abbott family I'm probably the last holdout for the traditional position," he added.
Mr Abbott's sister Christine Forster is a lesbian who has been with her partner Virginia Edwards since 2003.
The Liberal Party's current position it to oppose change to marriage laws, however Mr Abbott has left open the possibility of Liberal MPs getting a free vote on the issue in the future.
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