Celebrations have begun in Canberra, with the first same-sex couples legally married in the Australian capital.

The Australian Capital Territory's Marriage Equality Law came into effect at midnight, and 40 couples are registered to get married over the weekend.

The Australian national government challenged the validity of the laws, and the High Court will rule on the law's constitutional validity on Thursday.

This has opened a five-day window for same-sex couples to get married.

West Australia Labor MP Stephen Dawson married his partner of 10 years just after midnight on Saturday.

"This is about me and my partner tonight and our few close friends who've been able to join us," he said.

"This is about us, I guess professing our love for each other and reminding each other after 10 years that we still love each other and at least for the moment our relationship will be legally recognised as a marriage."