Australian Prime Minister Tony Abbott brushed off mounting pressure for a parliamentary vote on same-sex marriage from within his conservative coalition on Thursday, saying he was more focused on the economy and security.

A marriage equality bill is set to be proposed by a Liberal Party backbencher when parliament returns in August, seconded by an opposition Labor representative and with other co-sponsors from multiple parties, the Australian Broadcasting Corporation reported.

Abbott, a staunch Catholic who is against changes to the Marriage Act, acknowledged that same-sex marriage is an "important issue" but said the private member's bill is unlikely to be debated and voted on.