Last week the Senate approved the bill and rejected all proposed amendments that would have increased legal protections for those who would discriminate against gay couples on religious grounds.
Prime Minister Malcolm Turnbull, said he wants wedding celebrants, not just those affiliated with churches, to have the right to refuse to officiate at same-sex marriages.
He told Parliament, which resumed on Monday for its final two-week session of the year, that nothing in the bill threatened religious freedoms.
He explained: "We must not fail to recognise that there is sincere, heartfelt anxiety about the bill's impact on religious freedom.
"That is why I will support several amendments to the bill which will provide that additional reassurance in respect of their fundamental rights and freedoms."
The debated bill could soon legalise same-sex marriage in Australia as the major parties want the legislation passed this week after a majority of Australians endorsed reform in a postal ballot last month.
If the House of Representatives support Mr Turnbull's proposed amendment, then the altered bill would have to return to the Senate for ratification, delaying the reform.
Meanwhile, Tim Wilson, who is part of the conservative coalition, was among the first politicians to join the debate and used his speech to propose to his 33-year-old partner Ryan Bolger, a primary school teacher, who was watching from the public gallery.
Fighting tears, he said: "In my first speech I defined our bond by the ring that sits on both of our left hands.
"There's only one thing left to do: Ryan Patrick Bolger, will you marry me?"
A nonbinding postal survey found that 62 per cent of Australians resisted pressure from Church leaders by voting in favour of legalising same-sex marriage.
The 'Yes' vote on allowing gay couples to tie the knot won in all six Australian states, despite the most senior figure of the country's Anglican Church warning such a move would have "irreparable consequences" effects.
