But the Opposition leader says his remark has been misconstrued.
Mr Abbott's remark came after Prime Minister Kevin Rudd promised a conscience vote on a same-sex marriage bill by a re-elected Labor government.
It was this five second snippet of Tony Abbott in a Sydney radio interview that led to a social media storm.
"I'm not someone who wants to see radical change based on the fashion of the moment."
Marriage equality campaigners quickly went to work on Facebook and Twitter with that short quote put under images of the Opposition leader with the headline Tony Abbott on Marriage Equality.
The same-sex marriage activists and the Labor Party criticised Mr Abbott for what they claimed was his dismissal of same-sex marriage as being the fashion of the moment.
But the Opposition leader says his remark has been taken out of context, and he was speaking more broadly about his attitude to social change.
Before making the contentious remark, Mr Abbott reaffirmed on several occasions he supported the traditional definition of marriage as being between a man and a woman, adding that he'd always been clear and consistent.
He told the Sydney radio program that this sometimes created difficulties for him personally given that his sister Christine Forster is a lesbian who's in favour of marriage equality.
Tony Abbott said the last thing he wants to see is discrimination against anyone on the basis of race, religion, gender or sexuality.
But he pointed out that the parliament had looked at the issue and vote decisively against same-sex marriage.
After the interview, Mr Abbott maintained that this exchange with interviewer John Laws had gone from him giving his views on where he stood on same-sex marriage and the recent parliamentary vote to speaking more broadly about his attitude to social change.
"It really was quite a decisive vote and sure people can say let's reconsider this and who knows one day maybe the parliament will but I think people need to know or they deserve to know where I stand and I support the existing definition." (Laws) "Yeah, so do I and I see absolutely nothing wrong with tradition, many traditional things are wonderful and marriage is a tradition of very long standing and I like tradition and I think it's very important for a country like Australia to abide by some of those traditions." (Abbott) "Well, we have to be conscious of the fact that we are all products of the society, of the culture, of the circumstances that have shaped us and I'm not saying that our culture, our traditions are perfect but we have to respect them and my idea is to build on the strength of our society and I support by and large evolutionary change, I'm not someone who wants to see radical change based on the fashion of the moment."
Later, Tony Abbott acknowledged there are many Liberal Party MPs who have strong feelings on both sides of the marriage equality issue.
But he says a Coalition government would focus on what he called bread and butter* issues such as jobs, getting the budget under control and border security.
Someone who agrees in part with Tony Abbott is the founder of the National Marriage Coalition, Warwick Marsh.
"The electorate is saying immigration, the economy, education, health and everything but same sex marriage is an important issue so I'd actually disagree with Mr Abbott at this present moment, I think he's just trying to be diplomatic."
Warwick Marsh is also the founder of the Fatherhood Foundation, a group that believes chidren growing up without a father are at a distinct disadvantage.
"Fatherlessness has been shown to cause increases in young people committing crime, increased risk of going to jail, drug taking, health problems, more child sexual abuse, violence against our children, mental health problems, lower educational performance and an increased risk of child poverty."
But Warwick Marsh doesn't believe those challenges could be addressed if a child was brought up by two fathers because he's firmly against not only same-sex marriages but gay and lesbian relationships themselves.
And he argues homosexuality is a choice.
"What we're talking about here is a group of people that decide to choose a certain lifestyle and if they want to choose that lifestyle they have the prerogative to do so but they don't have the prerogative to inflict that lifestyle on everybody else. By actually redefining marriage, you actually destroy marriage because marriage by nature is a man and a woman."
Public opinion polls in recent years show a majority of Australians are in favour of marriage equality.
Prime Minister Kevin Rudd dropped his opposition to it earlier this year and made this promise during the first leaders' debate.
"My commitment to you is that within the first 100 days of a re-elected government, a bill would come forth to legalise marriage equality and on our side of politics we would allow a full conscience vote and I would appeal to Mr Abbott to do the same."
The call for a conscience vote is also coming from within the Coalition and one gay Liberal candidate in next month's election says there's broad support for such a vote.
Kevin Ekendahl is contesting the seat of Melbourne Ports and is promising to put a private member's bill to parliament should he be elected.
"Look, I'm not getting into politics to be a yes man for the Liberal Party. I'm getting into politics because I'm passionate about protecting my own local community, standing up for them and being a very strong local voice. Obviously in politics there's a lot of compromise but this is one particular issue where for me there is no compromise. This is an issue that is so important for so many people out there that I can put my hand on my heart and say I will absolutely, categorically, unequivocally, unashamedly be supporting marriage equality and fighting until we actually have full equality in the law for every Australian."
Another candidate vying for votes on September 7 says a conscience vote is called for.
The leader of the Palmer United Party, Clive Palmer told Channel 10 it's not for him to express a view one way or the other.
"And I don't want to influence people, I've told you our policy is that all Members of Parliament should have a free vote on the issue, it shouldn't be a party policy issue, that's our policy."
Bob Katter, the Member for the Queensland seat of Kennedy and leader of Katter's Australian Party is as well known for his oppositon to same-sex marriage as the Australian Greens are for their longstanding commitment to marriage equality.
