The committee's inquiry covered two bills supporting gay marriage, which will now be debated by a Parliament that has been reluctant in the past to consider ending the exclusively male-female legal definition.
Unless Abbott changes his mind and allows his MPs a conscience vote the latest bid also seems doomed.
The Labor Party last year changed its policy to support same-sex marriage, but on the insistence of Prime Minister Julia Gillard, an opponent of change, gave MPs the right to vote according to conscience rather than party line.
With Abbott refusing to allow Liberal MPs a conscience vote, the move is unlikely to succeed, a reality Greens deputy leader Adam Bandt recognised after the report was tabled.
Bandt, who with Tasmanian independent Andrew Wilkie proposed one of the two similar bills, said that he would now focus on changing Abbott's mind.
"If we try to hurry and push these bills to a vote too quickly, we run the risk of them being voted down."
Finance Minister Penny Wong, a gay senator, attacked Abbott for failing to uphold the "bedrock principle" of equality.
Federal law forbids same-sex marriage, although all states and territories recognise partners as de facto couples with the same legal rights as heterosexual counterparts.
The Australian Capital Territory performs civil unions, and gay couples are recognised in domestic partnership registries in Tasmania, Victoria and New South Wales, which last month urged the federal Parliament to legalise same-sex marriage.
NSW also allows gays access to assisted reproductive technologies and parentage recognition in altruistic surrogacy.
The federal Government has greatly widened legal recognition of gay couples, including tax-free superannuation benefits and laws covering tax, health, employment, aged care and social security.
The committee's report said neither of the bills advocating same-sex marriage would undermine existing protections such as age requirements, bans on relationships with family members, or the right of ministers to refuse to perform marriages.
Bigamy would remain illegal and adoption was a state issue.
The report said an on-line poll of more than 276,000 people showed 64 per cent support for legalising gay marriage.
But while the proposal has gained backing from a wide range of clergy, major religions continue to oppose same-sex marriage.
Sydney Catholic Archbishop George Pell sent letters to parishioners warning that the move would "radically reshape the cultural and social structures of our country".
The Anglican Archbishop of Sydney, Dr Peter Jensen, distributed similar messages.