The Brumbies take on the Otago Highlanders on Saturday against the backdrop of uncertainty surrounding the make-up of Super Rugby next season.
Although a final decision has yet to be made, proposals have been put forward which would see Australia lose one or more of heir five franchises as part of a reorganisation of the competition.
In response to media speculation surrounding the changes, the Brumbies said in a news release on Tuesday, the organisation were "asking the people of Canberra and the surrounding region to show their commitment to the team".
"The club is committed to a long future in this city," chief executive Michael Thomson said.
"We believe we are more than just a rugby team. We are proud representatives of Canberra and the region on the national and international stage.
"We have had several enquiries regarding the best way to show your support and passion for Brumbies Rugby and the best way to do that is through your action.
"By turning up to this weekend's match against the Highlanders to cheer the team on, you can help to show what the Brumbies mean to this city."
The Brumbies, who won the Super Rugby title in 2001 and 2004 and have made the playoffs the last four years, are Australia's most successful Super Rugby franchise by some distance and have produced an honour roll of Wallabies greats.
Although the Perth-based Western Force and Melbourne Rebels are more likely to face the axe if one is wielded, there has also been talk of merger between the Brumbies and the Rebels.
(Reporting by Nick Mulvenney; Editing by John O'Brien)
