Oslo police officer Paal-Fredrik Hjort Kraby said on Tuesday that the "United States embassy did not want to press charges".
As the US election campaign was in full swing in late October 2004, the group Gatas Parlament - whose name means "the parliament of the streets - called for donations on the website www.killhim.nu in order to pay anyone who succeeded in murdering Bush.
The US embassy had the site shut down and said at the time that it would press charges against the trio.
The group said the message was not supposed to be taken seriously and should have been seen as a public expression in the midst of a political campaign.
The three risked up to two years in prison.