Tony Abbott doesn't claim to be an overnight convert to a supporter of same-sex marriage but he is looking forward to attending his sister Christine's wedding.

Ms Forster is expected to marry her partner Virginia Edwards in February following a four-year engagement and a postal survey that supported their right to wed.

“I admire the commitment they (Yes campaigners) have brought to this long campaign and I accept that what they have fought for, for so long, should now come about,” Mr Abbott told parliament on Monday.

Mr Abbott has made no secret of his opposition to marriage equality and assured he would make sure the voices of four million Australians who voted no in the postal survey were heard.

"They are not bigots, they are simply people respectful of traditions handed down immemorial and slow to change them," he said.

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“It’s no secret that I haven’t been a supporter of same-sex marriage. I won’t be opposing this bill though as I respect the verdict of the Australian people as expressed in the postal plebiscite.”

The former prime minister again claimed credit for the survey, reminding parliament the plebiscite was an Abbott government idea supported by the Turnbull government and later all sides of parliament.

“To have a plebiscite was, in fact, an Abbott government decision… we opened the door to change, but ensured that change would not be lightly made.”

He also praised the respectful debate among those who had strong views on the issue.

"I am proud of my fellow 'no' campaigners because they gave marriage the good defence that it deserved, but I do congratulate the 'yes' campaign on their victory," he said.

"There was a lot said beforehand about how divisive this debate would be but from where I stood there was little rancour, no hysteria and no abuse, certainly there was none from the 'no' campaign."

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Despite his opposition, Mr Abbott will support a cross-party bill to allow same-sex couples to marry which the Senate passed last week.

“I certainly don’t pretend to be an overnight convert to supporting same-sex marriage, but I pledge to respect the verdict of the Australian people. Same-sex marriage should now be recognised.

"I am looking forward to attending the marriage of my sister Christine to her partner," he added.

But Mr Abbott moved a small amendment that would have the House note "that it is vital that individuals and entities are not disadvantaged nor suffer any adverse effects as a result of conscientiously holding a particular view of marriage".

Mr Abbott said further amendments on religious freedoms should be addressed with the bill to ensure there were no gaps in the protection of fundamental freedoms.