The open letter to Prime Minister Blair appears in the current issue of parliament's The House magazine, and in it the film's distributor, Optimum Releasing, issues an invitation to the PM for a private screening.
It is part of a media campaign planned and bought by Target NMI to promote the film ahead of its launch next week.
There will also be laser projections on unnamed significant buildings, in the style of Gail Porter's appearance on the Houses of Parliament, but using an image of the filmmaker Moore. There will also be advertisements in the national press and outdoor, playing up the film's controversial side.
Traffic to the film's rose by 343% in the two weeks leading up to the film's US release on June 25, according the online intelligence group Hitwise, and on the day of release it was the top official move site in the Hitwise movies category.
Furthermore, traffic to has increased by 148% since June 12, making it the seventh most visited political site in the UK.
'Fahrenheit 9/11' looks at the events of September 11 and the reaction of the Bush administration, including subsequent invasion of Iraq. The controversy stems from the examination of issues such as why Bush avoided pursuing the Saudi connection to 9/11, despite the fact that 15 of the 19 hijackers were Saudis.
The film won the Palm d'Or at this year's Cannes Film Festival, and became the first documentary in history to top US box-office charts for its first week. 'Fahrenheit 9/11' opens in the UK on July 9.
Moore is already a controversial figure in the US and was booed when he collected his Oscar for best documentary for the film 'Bowling for Columbine', after saying "Shame on you Mr Bush" during his speech.
The film has been heavily criticised in the US by supporters of Bush, who say that the film twists and misrepresents facts to make its case, including the central claim that Saudi Arabian interests have given $1.4bn to firms connected to the family and friends of Bush.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the .