"From the outset I have made a conscious decision to try and keep this matter private and not discuss it in the press. While my wife and I are dissolving our marriage, we will work together to parent our two children," he says of sons Mason, 6, and Jake, 2. "I love my boys very much. I want only the best for them and am committed to being a devoted father."
The CSI: Miami actor's statement, issued Thursday, comes after Rimes and Cibrian went public with recent dates, including a game of golf and a Kings of Leon concert. Earlier this week Cibrian filed for divorce from former model Brandi Glanville, citing irreconcilable differences.
Glanville has talked about her heartbreak over the demise of her marriage and said she sensed the attraction between her husband and Rimes when they filmed their Lifetime movie Northern Lights last fall. But Cibrian insists: "I will continue to be respectful and sensitive to this issue by not doing interviews about this ongoing private matter. I wish everyone would do the same."
For more on Rimes and Cibrian's recent dates – and how their exes are reacting – pick up the current issue of PEOPLE, on newsstands now