Liberal leader Abbott, speaking on Sydney radio station Radio 2SM, referred to same-sex marriage as a "fashion of the moment."
Media criticized him for saying during a hustings visit that a female Liberal candidate had "sex appeal."
Abbott, 55, is known for his traditional views on marriage and told Radio 2SM that he viewed marriage as between a man and a woman.
The discussion centered on tradition in Australian society, the Australian Broadcasting Corp. reported.
"My idea is to build on the strength of our society and I support, by and large, evolutionary change," Abbott said. "I'm not someone who wants to see radical change based on the fashion of the moment."
Abbott later backtracked, saying he wasn't suggesting gay marriage was a passing fad.
"We'd really moved beyond the subject of same-sex marriage in that discussion," he said.
"We were talking about tradition more generally. The point I was making really was that conservatives tend to hasten slowly, regardless of the issue."
The gaffes come as Abbott's alliance of the Liberal Party and several small parties -- which is slightly ahead in the polls -- is fighting hard the governing Labor Party to win a federal election Sept. 7.
ABC reported Labor Deputy Prime Minister Anthony Albanese was quick to pick up on Abbott's gender references.
Albanese told ABC News 24 Abbott's reference to same-sex marriage was an "extraordinary comment" and "deeply offensive to many Australians."
The Age reported Abbott's latest controversial statements "add to an archive that includes statements including that abortion was the 'easy way out' and his suggestion that women may not have the right physiology for public life."
During a tour of Sydney to support Liberal candidates in their ridings Tuesday, Abbott said Fiona Scott, the coalition's candidate for Lindsay in western Sydney, had "sex appeal."
But he also was quick to say she was "very connected with the local area."
Abbott is hoping to unseat Prime Minister Kevin Rudd and his Labor government that he took over winning a leadership challenge.
Rudd, 55, aims to repeat his successful 2007 election victory. However, his victory turned into a personal defeat when his Deputy Prime Minister Julia Gillard won her leadership challenge in 2010.
Soon after Gillard as prime minister went to the polls, but the country elected a hung Parliament.
Labor and the opposition coalition group of the Liberal and National parties each won 72 seats in the 150-seat House of Representatives.
Labor has led a minority government thanks to support from the Green Party member of the House and three independents.
Rudd needs a Labor win to legitimize his leadership.
But a Newspoll published Monday in The Australian newspaper put Liberals ahead at 52 percent against Labor's 48 percent on a two-party basis -- the same as a week ago.
Voting is compulsory in Australia's national, state and territorial elections.
Initially, the Australian Electoral Commission will write to suspected non-voters requesting that they either provide a reason for their failure to vote or pay a $20 penalty.