The Canadian city and New Delhi both formally lodged bids with the Commonwealth Games Federation in London on Friday. A final decision will be made by member nations at a general assembly in Jamaica in November.
Hamilton, which staged the first Games in 1930, plans to introduce football while New Delhi wants to re-introduce cricket.
Cricket featured in Kuala Lumpur in 1998 but not at last year's Manchester Games.
New Delhi, hosts of the 1951 and 1982 Asian Games, is seeking to stage the event in the Commonwealth's largest country.
The Games' new programme, which limits the maximum number of sports to 15 with a minimum of 10, will be introduced in 2010. Melbourne will host the 2006 Games.
