Suri now lives primarily in New York City with Holmes, who has been in South Africa filming "The Giver," with Taylor Swift. Holmes brought her daughter with her to South Africa and the pair were spotted together in Cape Town last month, according to a report in Us Weekly magazine.
Bauer Publishing filed court documents of its own in the case, writing that, at the time of publishing, Cruise had not seen his daughter in 44 days. The company claims Cruise was out at clubs and bars and vacationing, when he could have been with his daughter.
If Cruise prevails in his lawsuit, it would mark the first time the actor has successfully sued tabloids for stories involving his children, who, in addition to Suri, include a son and daughter with actress Nicole Kidman.
ABC News reached out to representatives for both Cruise and Holmes, but neither immediately responded.
Cruise's attorneys did not immediately respond to ABC News' requests for comment, and neither did representatives from the Church of Scientology.