Same-sex couples could know by the end of this week if they are able to marry under the ACT's marriage equality law.
A two-day hearing of the federal government's challenge to the ACT government's law will begin in the High Court on Tuesday.
The ACT government expects the court will reach a decision this week before the first marriages can take place on December 7.
The government said it had registrations for 47 couples who plan to marry in the ACT. The Commonwealth is challenging Australia's first same-sex marriage law, which it argues is inconsistent with the federal Marriage Act and the Family Law Act.
The case is the country's first real test of whether states or territories can legislate for same-sex marriage.
Federal Attorney-General George Brandis has described the ACT law as ''a threat'' to the ''well-established position'' that there should be nationally consistent laws for marriage. The Abbott government will argue that the federal marriage laws provide an exhaustive definition for marriage and that the ACT government is acting outside of its legal scope as a territory.
But the ACT believes its same-sex marriage law can operate concurrently with the federal laws because it applies to a separate status of marriage.
The ACT government scrambled to reword its bill before it passed the Legislative Assembly in October to try to strengthen its chances of surviving the High Court challenge.
ACT Attorney-General Simon Corbell said on Monday the government was approaching this ''very important case'' with ''a level of apprehension''.
''I'm confident in the strength of our arguments,'' Mr Corbell said.
Mr Corbell said he believed a finding would be made in the case this week.
Advocacy group Australian Marriage Equality will seek to intervene in the case on Tuesday in defence of the ACT law.
Anna Brown, director of advocacy at the Human Rights Law Centre, said as well as testing whether the states and territories could legalise same-sex marriage, she hoped the case would clarify whether the constitution permitted federal Parliament to legalise same-sex marriage.