Advocates and some constitutional law experts argue that poor drafting by the ACT government contributed to the High Court's unanimous decision on Thursday to declare the ACT marriage equality law unconstitutional.

They say that the judgment does not preclude states and territories from trying to enact differently worded same-sex marriage laws.

But the ACT government said the court had ruled clearly and unambiguously that only the Federal Parliament had the jurisdiction to decide if Australia should have same-sex marriage.

Chief Minister Katy Gallagher said the court had now planted the issue ''firmly at the feet'' of the Abbott government, before calling for all federal MPs to be given a conscience vote.

''Over to you, Mr Abbott,'' Ms Gallagher said. ''This is not a campaign he can avoid.''

Thirty-one couples who married in a five-day window under the ACT law have had their marriages declared invalid.

But in a significant step for marriage equality supporters, the High Court ruled the Federal Parliament did have the power to enact same-sex marriage laws.

Constitutional law experts said that the court's decision had not ruled out further attempts by states or territories to pass laws that created a distinct legal status for same-sex marriage.

However, the task of creating a bill that could survive challenge was now more difficult because of Thursday's result.

Constitutional law expert Professor George Williams was among marriage equality advocates who had previously argued for an ACT law that more clearly created a separate type of marriage for same-sex couples.

''The High Court did pinpoint some of the drafting issues with the ACT bill,'' he said. ''It wasn't the only reason they lost but it was one significant factor.''

The High Court had ''made no statement about a differently drafted bill'', leaving the question open as to whether the West Australian, NSW or Tasmanian bills could survive.

''The only thing this does is say you can't have a territory or state attempt to achieve this form of marriage equality,'' Professor Williams said.

Australian Marriage Equality director Rodney Croome said the court had ''identified precisely the problem that we raised with the ACT government before the act was passed''.

Federal Greens leader Christine Milne said the territory's leaders should have listened to legal advice about the final format of the same-sex marriage law before it passed the Legislative Assembly in October.

The ACT government, however, said the judgment found ''clearly and unambiguously that the only parliament in the land that can deal with marriage law is the Federal Parliament''.

"I don't want to get into a fight with people who are on the same side of this debate," Ms Gallagher said.

"But there is absolutely nothing in the decision that says this was about language."

A same-sex marriage bill, with different language to the ACT law, was introduced into the West Australian Parliament on Thursday by Greens MP Lynn MacLaren.

That bill has the same wording as same-sex marriage bills introduced in other states.

The High Court ruled Australia's first same-sex marriage law was invalid because it was inconsistent with the Federal Marriage Act.

The court held the ACT's act provided for marriage equality for same-sex couples, not, as the territory argued, for a form of legally

recognised same-sex marriage that was different from marriage as defined by federal law.

The court delivered its findings to a silent court room, some couples sobbing quietly as Chief Justice Robert French read the unanimous ruling.

The court found the Federal Marriage Act was a ''comprehensive and exhaustive statement of the law of marriage''.

The High Court ordered the ACT to pay the Commonwealth's legal costs.

The bill is expected to run to tens of thousands of dollars.

Australian Christian Lobby managing director Lyle Shelton described the judgment as a decision for commonsense.

ACT Liberal leader Jeremy Hanson, who opposed the marriage equality law, said the court had made it clear that marriage was a matter for the Federal Parliament.