Same-sex couples fall on the wrong side of a ‘‘binary divide’’ in  law and must remain unmarried people, the federal government says.

The  government on Wednesday filed written submissions on its challenge to the ACT’s same-sex marriage laws in the High Court.

The submissions reveal the federal government will challenge the ACT law on several grounds, including conflict with the Marriage, Family Law and ACT Self-Government acts.

The ACT established the country’s first same-sex marriage laws last month, but the federal government  launched a constitutional challenge the day after the historic legislation was passed.

The High Court agreed to hear the challenge next month – before any marriages can take place – and set the parties deadlines to file written submissions.

Australia’s second legal officer, Commonwealth Solicitor-General Justin Gleeson, SC, lodged the federal government’s submissions on Wednesday.

The documents argue the federal government  had the power to legislate a single and uniform ‘‘rule for Australian society as to what constitutes a valid marriage’’.

The key constitutional issues in contest are whether the ACT’s bill conflicts with the Federal Marriage Act, which defines marriage as being between a man and a woman, and the Family Law Act, which governs issues such as divorce.

The submission said the ACT Act contradicts the two federal acts as there was no room for both national and regional laws on the issue.

The ACT attempted to create a distinct and separate type of marriage that could sit alongside the federal laws.

But the federal government’s submissions said the Marriage Act did not permit the territory to ‘‘purport to clothe with legal status of marriage a union of persons, whether mimicking or modifying any of those essential requirements of marriage’’.

‘‘The Marriage Act is thus an expression by the Parliament that, within the field of its sovereignty, the binary division in status between married and unmarried will be demarcated by ... that Act,’’ the submission said.

‘‘Couples who are not man and woman ... remain on that [unmarried] side of the binary divide.’’

That interpretation was strengthened in 2004 when the Howard government amended the act to provide the definition of marriage as the union of a man and a woman.

The submissions also argue the ACT’s Marriage Equality Same-Sex Bill was inconsistent with ACT Self-Government Act, which says any territory law which affects a law of the Commonwealth is void.

The ACT now has until November 25 to file its submission, with the federal government then given until  November 29 to reply.

The case will be heard by the full bench of the court on December 3 and 4 – before the first marriages can take place under the ACT’s newlaws.

Mr Gleeson estimated the government’s oral argument would take about 3 hours.