Cruise has seldom spoken about his divorce from actress Katie Holmes in June 2012.
But he defends his relationship with their 7-year-old Suri in the $50 million lawsuit he recently filed against the magazines, which alleged he walked away from the girl when he and her mother split up, TMZ reported.
"I have in no way cut Suri out of my life -- whether physically, emotionally, financially or otherwise," Cruise wrote, adding he saw his daughter in person numerous times in the months following the divorce.
"Even during the times when I was working overseas and was not able to see Suri in person, we were [and continue to be] extremely close," the actor said.
"As my numerous emails with Suri's mother during this time period demonstrate, I was a constant presence in Suri's life," he said, referring to how he worked on two films back-to-back shortly after Holmes left him. "While I'm sure my daughter misses me when I am not with her [as I miss her], she is a very happy child, and we have a wonderful relationship and cheerful phone calls."