The Prime Minister reiterated his opposition to legalising same-sex marriage in Australia and would not commit to a conscience vote for his MPs and senators if a bill came before the Federal Parliament.

But marriage equality advocates said on Friday they believed national reform of marriage laws was still achievable, following earlier comments by senior cabinet minister Malcolm Turnbull that Coalition MPs were likely to be given a conscience vote.

Australian Marriage Equality, the key lobby group in the fight for same-sex marriage, also called on state and territory parliaments to continue their attempts to legalise same-sex marriage, despite the High Court's ruling that the Federal Marriage Act was a ''comprehensive and exhaustive statement of the law of marriage''.

Mr Abbott said the High Court's ruling on Thursday had not been formally discussed at Friday's Council of Australian Governments meeting with premiers and chief ministers in Canberra attended by ACT Chief Minister Katy Gallagher.

Ms Gallagher's office said the Chief Minister had a brief conversation with Mr Abbott during which she reiterated comments that the matter was now squarely before the Federal Parliament.

Mr Turnbull earlier raised the possibility of a conscience vote for Coalition MPs on gay marriage but Mr Abbott was non-committal in the post-COAG news conference.

''Plainly, as a result of the decision of the High Court yesterday, it is a matter, should it be changed, for the Federal Parliament,'' the Prime Minister said. ''You know my position, I don't think it should change and I suspect that even up here among my fellow first ministers, there will be a range of views.

''If we have a bill come before the Parliament, it will be dealt with by the Coalition in the usual way, we will have a discussion and we will come to a position on it.''

Mr Abbott said the High Court decision was ''disappointing'' for couples who wed in Canberra at the weekend under the ACT's now defunct same-sex marriage laws, but that they knew the risks of the pending court action by his government.

Thirty-one couples who married in the five-day window have had their marriages declared invalid. ''They knew there was this possibility that their marriages might fall foul of the High Court and obviously it is disappointing for them,'' Mr Abbott said.

Australian Marriage Equality director Rodney Croome said the High Court had reignited the push for national reform by removing the question that hung over the Federal Parliament's power to pass marriage equality laws. ''We agree wholeheartedly with former Liberal leader Malcolm Turnbull that it is possible for marriage equality to occur under an Abbott government, as long as a conscience vote is granted,'' he said.

Some constitutional law experts, including George Williams, also argue that the High Court judgment does not close the door to further attempts from state and territory governments to try to legalise same-sex marriage. The ACT government is likely to reintroduce its civil unions laws.

Australian Marriage Equality said the territory government should preserve its ''newly minted status as the rainbow territory'' by trying to pass a redrafted same-sex marriage bill, written in consultation with legal experts and the community.