The current issue of the tabloid has a cover referring to the Oblivion actor's "House of Horrors", and claims that he was behind "abuse", "punishments" and "humiliation".
Allegations made within include the claim that Suri was made to stay for five months in a "tiny, windowless room".
The Hollywood Reporter has posted a letter sent on July 11 by Cruise's lawyer Bertram Fields to American Media, Inc, describing the article as "disgraceful and lurid" and "riddled with lies".
The letter goes on to claim that the story will cause Cruise "hundreds of millions of dollars of professional and personal damages, for which [Cruise's team] intend to hold American Media, and everyone who participated in the perpetuation of this scurrilous attack, jointly and severally liable".
Referring to the cover's allegation that Tom Cruise is a "monster", Fields wrote: "Mr Cruise is certainly not a 'monster'. He is a caring father, a hardworking actor and, above all, an honest, decent man."
The letter ends with a demand for the National Enquirer to retract "each and every one of [its] false assertions".
Recent reports about Cruise's split with Katie Holmes have included the claim that the actress used a secret phone to plan her divorce, and turned to both Nicole Kidman and Victoria Beckham as confidantes.
Photo gallery - Tom Cruise and Katie Holmes: