Eric Abetz has warned that a cross-party bill to legalise same-sex marriage could open a "Pandora's box" and lead to polygamy.
The Senator told ABC Radio criticised media coverage of the issue and cited the "Asian century" as a reason for not moving on marriage equality.
"Tell me how many Asian countries have redefined marriage?" he said.
"... Are we in the Asian century or not? It's amazing how certain people try to pick and choose in relation to debates. All of a sudden the United States, which is usually condemned, is now being celebrated on the bizarre decision of a five-four majority in the Supreme Court."
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Interactive: Where does your local politician stand on same-sex marriage?
Senator Abetz also implied that ministers who supported gay marriage should resign, citing his decision to quit the opposition frontbench in 2009 over support for an emissions trading scheme.
"As a frontbencher you have to support party policy," he told Sky News.
Prime Minister Tony Abbott said the issue was important, but added "I'm not sure that it's the only talking point, or even that it's the biggest one".
Addressing media on Thursday, Mr Abbott said the government would remain focused on growth and security issues instead.
"This government was elected to grow jobs, to promote the stronger economy, to secure our nation against the various challenges that we face at home and abroad, and that's what we are doing," he said.
"As far as I'm concerned, that will always be the focus of this government."
Mr Abbott said it was "quite unusual" for for private members bills to come on for debate and vote in parliament.
'Anyone who thinks that this should be prioritised over economic or national security issues has rocks in their head'
Some of his colleagues have been more vocal in their opposition to the bill, including frontbencher Concetta Fierravanti-Wells.
"Any change of this magnitude requires appropriate consultation and not the sort of ambush approach some of my colleagues have chosen to take," she told ABC radio on Thursday.
Liberal Warren Entsch, backed by colleague Teresa Gambaro, is planning to introduce marriage equality legislation to parliament in August.
Whether the bill - backed by several Labor MPs, the Greens, and independents Andrew Wilkie and Cathy McGowan - is debated in the lower house is up to a selection committee.
One of its members, Liberal MP Andrew Nikolic, argues that it won't be on the agenda any time soon.
"Anyone who thinks that this should be prioritised over economic or national security issues has rocks in their head," he said.
Senator Cory Bernardi, a staunch opponent of change, believes the government shouldn't be sidetracked by the issue.
"If my colleagues choose to participate with Labor and the Greens in derailing the government's agenda, that's up to them, but I wouldn't be endorsing it," he told ABC radio.
But Liberal backbencher Ewen Jones, who backs a free vote on the issue, called for the bill to be debated as quickly as possible, rather than pulling the bandaid off "one hair at a time".
Labor frontbencher Penny Wong said it was unfortunate the prime minister kept "putting up different obstacles to marriage equality coming to a vote" .
Mr Abbott's sister Christine Forster, a Liberal Sydney city councillor, hopes the issue is dealt with soon, warning there could be consequences at the polls for the coalition.
"Why would we want to get into a federal election campaign in which we are perceived by 70 per cent of the electorate as being the road block to a reform," she told 2GB radio.
Opposition MP Terri Butler, one of the bill's co-sponsors, hopes more MPs will come out in favour of change, saying it had cross-party support".
The Australian Christian Lobby warned against the redefining marriage, arguing children should have a mother and a father.
