"We are committed to working together as parents to accomplishing what is in our daughter Suri's best interests. We want to keep matters affecting our family private and express our respect for each other's commitment to each of our respective beliefs and support each other's roles as parents," read the statement to ABC News from their reps.
Sources close to the case tell ABC News that the focus is on Suri and that "both sides in the case have said from the beginning that she is their main concern."
Holmes, who filed for divorce from Cruise last week, is seeking sole custody of their six-year-old daughter, Suri.
In a case of art imitating life, the actress' next film role will be playing a single mom.
Next week, Holmes, 33, is scheduled to start production on her new film, "Molly," about a single mother and her daughter, according to People magazine. Holmes co-wrote and is co-producing the film.
Showbiz411.com, however, is reporting that the project is on hold for now.
Despite the divorce, Holmes, who recently taped a guest appearance on "Project Runway," has been keeping busy.
This last week, pictures poured in of Holmes and her daughter out and about in Manhattan enjoying ice-cream, a museum, popping into Whole Foods and visiting her attorney this weekend.
The actress, who is expected to wrap filming on her latest movie by August, is also busy planning her first-ever show for her clothing line, Holmes & Yang, at New York's Fashion Week in the fall. Also this fall, she is due to shoot "Responsible Adults," a romantic comedy with Chace Crawford.
Amid her busy schedule, Holmes and Cruise are quietly trying to work out a divorce settlement.
Sources close to case tell ABC News that both Cruise and Holmes "want to settle this matter privately and that talks are ongoing between the two parties."
While the first hearing in the case is set on the New York Civil Supreme Court calendar for July 17, that is a full week away. Both parties have stated they want what's best for their 6-year-old daughter Suri and sources close to the case told ABC News that "they have never ruled out trying to reach an amicable settlement."
They are now trying to do just that.
Robert Stephan Cohen, who has represented celebrities Christie Brinkley, James Gandolfini and New York City Mayor Michael Bloomberg in their divorce cases, told ABC News that if "this case goes through the court system in New York or California it would be very complicated."
Cohen, who also serves as an adjunct professor at the University of Pennsylvania, said that what happens to the child going forward would be the big issue in any kind of settlement talks.
"The parties can decide what school she can go to and who her pediatrician is but what about Scientology?" he said. "Is he willing to forgo having his daughter raised as a Scientologist? Is she willing to allow the child to be one? If they can work those issues out they may be able to work out a deal."
Holmes filed for divorce and sole custody of the couple's daughter on June 28.
Since then, Cruise, 50, has kept a low profile. Sources close to the actor admitted that Cruise was "stunned" by Holmes' action, which his publicist said left him "deeply saddened."
He returned to Los Angeles from filming in Iceland last Tuesday to celebrate what was described as a "somber" 50th birthday celebration with his family.
Sources close to the actor said they were fine with letting Holmes play the "media game" last week because that is exactly what Cruise wanted. But make no mistake, Cruise has not really been quiet. He has been strategizing with his team of lawyers and calling the shots on what to do about what his associates say "came out of nowhere."