"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."
Some legal analysts have said that Holmes' decision to file for divorce in New York might have given her an advantage in her effort to gain sole custody versus joint custody and provide more privacy, since New York seals divorce filings that are often available in California.
California divorce attorney Michael Kelly told The Associated Press that Holmes' East Coast filing was "a tactical move" that signifies "there will be an attempt to gain an advantage."
New York's comparative-fault divorce laws could be advantageous for Holmes, he said. The couple spent most of their marriage in Los Angeles but Holmes has been in New York for most of this year.
Holmes dumped her longtime security team because of their loyalty to Cruise, according to sources, and there had been lots of talk about what is really no longer the elephant in the room, Scientology.
The Church of Scientology issued a statement denouncing reports that Holmes and Suri have been followed by members of the church -- reports that were debunked when it became clear that Holmes' own security people were outside her building.
Nobody from the Cruise camp has uttered the word Scientology publicly yet, and a source who reviewed the divorce complaint says there is nothing about scientology in the document that Holmes filed on June 28.
But sources close to the case did acknowledge that Scientology is an issue for Holmes and one person close to actress said it has been for some time, despite appearances.
Cruise Has Gone Settlement Route Before
The previous times Cruise has gotten divorced, he was in control.
Curiously all of Cruise's marriages ended when his ex-wives were 33 years old.
Cruise filed for divorce from his second wife, Nicole Kidman, in February 2001, sometime after she miscarried their baby, according to Kidman (they had previously adopted two children).
He filed for divorce less than two months after they renewed their vows on their 10-year anniversary, Christmas Eve 2000.
Kidman broke down on Oprah Winfrey's talk show in May 2001, calling the situation a "nightmare."
"I think that divorce is hard for anyone. It's a nightmare, it just is, and you can pretend you're fine," she said. "And days you're great [and] days you're not great."
In a written response to a divorce petition filed by Cruise on the grounds of irreconcilable differences, Kidman said she was stunned when he told her that he no longer wanted to be married, and allegedly begged him to stay and seek marriage counseling. He refused and left for good, according to her response.
When asked by Winfrey whether she thought she would always be married, Kidman timidly replied, "Yeah."
"I've had a blessed life," she said. "I've always thought [if] something bad is going to happen, something bad is going to happen.
But then something really bad happened. A number of really bad things happened. You go, 'I'm dealing with it. I'm stronger than I thought.'"
Kidman is now happily married to country singer Keith Urban. They have two children together. Connor and Isabella Cruise chose to live with their dad after the split, which was settled out of court.
Given how adoringly Cruise has spoken about Katie Holmes throughout their relationship -- he told the May issue of Playboy, "I'm just happy, and I have been since the moment I met her" -- he may take a while to get back to his eccentric, couch-jumping self. But his first ex-wife once voiced her confidence in Mr. Mission Impossible's ability to rebound.
"Tom is very strong -- he handles stress," Mimi Rogers told People magazine in 2001. "He's human. He has a temper. He blows up sometimes, whatever, but it's not like he can't deal with it."
He filed for divorce from actress Mimi Rogers in January 1990 after three years of marriage.
She seemed to get over it quickly. In October 1990, she told The Associated Press, "As far as I know, we're divorced, but I've been so busy on this new film that I haven't had time to check, so I'm not sure. I bet that sounds pretty silly, huh?"