The letter, purportedly from a group calling itself "We who built Sweden", also warned of further attacks unless Stockholm withdrew its bid for the games. "We are the ones who burn and blow up sports arenas," the message said. "We have large reserves of explosives, automatic weapons and ammunition. Do not doubt our determination and ability."
But Swedish police said the note was probably not written by those who were responsible for the blast - the eighth attack against sports arenas in Stockholm since the government gave financial backing to Stockholm's bid in May.
"The contents suggest that someone else has written the letter, but it's hard to tell before the security service has analysed it," Stockholm policespokesman Claes Cassel told TT.
Police were comparing the letter with several arson and bomb threats against malls in Swedish cities during the Christmas shopping season.
Stockholm's chief of police, Sune Sandstroem, also denied a link between the letter and the arson attacks. "It would have been sent earlier if there was a clear connection to the bid," Mr Sandstroem said.
No one was hurt in Friday's predawn explosion, which scattered glass, roof tiles and debris from the 1912 arena - the world's oldest Olympic stadium still in regular use.
Yesterday's note attacked the cost of the Games. "If Sweden is to arrange the Olympics, everyone involved in the preparations and arrangements will be our targets. This includes athletes and audiences," it said.
Opponents of the bid claim the Olympics would drain more money from Sweden's cradle-to-grave welfare system, which has been suffering cutbacks in recent years.
Politicians and sports officials publicly said the bombing would have no effect on Stockholm's chances of winning the bid to arrange the games, but the Aftonbladet newspaper summed up what many people feared. "End of the Olympic Dream," a front-page headline said at the weekend.
The International Olympic Committee is to decide on 5 September which city will organise the 2004 Olympics. The other candidates are Buenos Aires; Argentina, Cape Town; South Africa, Athens; Greece and Rome.