Tom Cruise Wants Suri's Life to Be 'As Normal As Possible,' Says Source

07/20/2012 at 08:30 AM EDT

Since Katie Holmes filed for divorce from Tom Cruise, their daughter Suri's world has changed.

But her father, who will get generous visitation with Suri who will live primarily with Holmes, is determined to minimize the disruption to the 6-year-old's life.

"He's going to try, despite all the attention, to have things be as normal as possible," a source tells PEOPLE.

Cruise, who had been filming the movie Oblivion in California, arrived in New York City on Tuesday. He was photographed carrying Suri into a Manhattan hotel and later taking her to a gymnastics lesson. The father-daughter pair were then seen taking off in a helicopter together on Wednesday.

PHOTOS: Katie & Suri's Life in the Big Apple

Says the source: "It's going to be challenging" for Cruise who is suddenly a single dad.

"But he's going to have a meaningful relationship with her, as he always has," the source continues. "[Suri will] visit him on movie sets when she's not in school. He'll call her all the time."

For much more on this story, including details on Tom's trusted inner circle, how he’s coping and Holmes's new life, pick up the new issue of PEOPLE, on newsstands now

PHOTOS: The Holmes-Cruise Family in Happier Times