Glasgow, the Nigerian capital Abuja and Canadian city Halifax are vying to host the 2014 Commonwealth Games.
McConnell said Glasgow's bid "can inspire Scotland"
The three bids were confirmed on Sunday by the Commonwealth Games Federation (CGF) ahead of Wednesday's opening of the 2006 Games in Melbourne.
The successful city will be announced at the CGF General Assembly which takes place in Sri Lanka in October 2007.
In 2010, Delhi will become the first city on the subcontinent to stage the Commonwealths Games.
The Glasgow bid team staged a video presentation for the CGF in Melbourne ahead of the start of the 2006 Games on Wedneday, 15 March.
Scotland's First Minister Jack McConnell said: "For a city as important as Glasgow never to have held the Games is a wrong that needs to be righted.
"It is one of the best sporting cities in the Commonwealth."
McConnell said Glasgow's bid budget - reported to be around £300m, including £250m government funding and £50m in sponsorship - had been "carefully costed".
He added: "There is a case for the Games to go to Africa at some point, but I think that Glasgow is the strongest of the three 2014 bids."
The Scottish bid will include a new-build Games Village capable of housing
6,000 athletes and officials, a National Indoor Sports Arena and a National
Velodrome, the latter two to be completed in 2010.
Existing venues to be utilised include Hampden Park (opening and closing
ceremonies, athletics and rugby sevens), Tollcross Park Leisure Centre
(swimming), and the Scottish Exhibition and Conference Centre (netball and other indoor sports) and Kelvington Park (lawn bowls).