The dispute over the ACT's same-sex marriage law, dubbed a ''David and Goliath battle'' by the territory government, appeared in the High Court for the first time on Friday.

A full hearing of the matter could occur as early as the first week of December, throwing into doubt whether any weddings could occur before the challenge is heard.

The federal government, as expected, pushed on Friday for the hearing to be scheduled as soon as possible, arguing it should occur before the end of the year.

But the ACT government said the proceedings should not be rushed in a way that would prejudice the parties.

High Court Chief Justice Robert French instead adjourned the directions hearing until early next month, suggesting a hearing could be set down for the first week of December.

Prime Minister Tony Abbott and Attorney-General George Brandis have called on same-sex couples to delay getting married until the High Court battle is resolved, arguing it would cause "distress" if the laws were overturned and marriages declared invalid.

It was suggested in court that the first marriages under the laws could take place from December 7.

The ACT has 10 working days to gazette the law, which leaves a chance the law could take effect from the beginning of December if the legislation is processed quickly.

Same-sex couples remain hopeful this will prove the case, but ACT Attorney-General Simon Corbell said on Friday it was unlikely the first marriages could take place before December 7.

The High Court would not necessarily make a ruling at the conclusion of the full hearing and could reserve its judgment.

Chief Justice French asked the ACT to file a defence by early next month, with the court expected to sit again for directions on Monday.

The key constitutional issue is expected to be whether the ACT's Marriage Equality Same-Sex Bill is inconsistent with the federal Marriage Act, which defines marriage as being between a man and a woman, or the Family Law Act, which deals with issues such as divorce.

If the laws are inconsistent, they are likely to be deemed unconstitutional and declared invalid.

The federal government launched its constitutional challenge on Wednesday, just one day after the bill was passed by the ACT Legislative Assembly. Mr Brandis said on Friday he would not be commenting while the matter was before the court.

Mr Corbell said Friday's hearing had played out "as expected" but it would be inappropriate to comment further.

Australian Marriage Equality deputy director Ivan Hinton said on Friday he remained hopeful that the first weddings could occur before the challenge was heard.

Mr Hinton married partner Chris Teoh in Canada five years ago but the couple plans to marry again on home soil under the new ACT law. "It's a very rare situation for an Australian to propose to another Australian and find less than a week later that that … opportunity of celebrating that relationship is going to the High Court," Mr Hinton said. If the High Court were to strike down the law it would be "very, very hard for many Australians to understand," he said.

The ACT is attempting to create a distinct and separate type of marriage that can sit alongside the federal marriage laws.

The ACT government was forced to make changes to the laws on Tuesday to strengthen its case in the High Court. The government is under pressure to make further changes before the High Court hearing.