The 51-year-old filed a defamation lawsuit against a magazine publishing company in 2012 over the claims.
New documents filed in court Tuesday by the celebrity demand that Bauer Publishing Co. reveal their sources or admit to fabricating reports about his parenting role.
Last year, "In Touch" and "Life and Style" magazine wrote articles claiming Cruise "abandoned" Suri. The stories in Life & Style and In Touch magazines cited Cruise's absence from Suri's life due to overseas film shoots. The stories were picked up by a plethora of news outlets.
"I have in no way cut Suri out of my life - whether physically, emotionally, financially or otherwise," Cruise wrote in the documents filed Tuesday.
He said despite filming back-to-back movies in the second half of 2013, he spoke to his daughter nearly every day and got frequent updates about her from her mother, actress Katie Holmes.
Cruise's attorney, Bert Fields, says the actor is a caring father, and Suri is a "vital part of his life."
In response, Bauer's lawyers are asking for a protective order which would allow them not to answer to Cruise.
The company has also turned over files to Cruise's legal time that describe the magazine's reporting and statements from confidential sources. These sources allegedly said the actor had missed Suri's first day of school and could have flown to New York to see her.
A hearing is scheduled for Nov. 26.
The Associated Press contributed to this report.