LeAnn Rimes’ flame asks for privacy

(People.com)

– After filing for divorce from his wife, actor Eddie Cibrian — who is now romancing country star LeAnn Rimes — is asking for privacy and saying he remains committed to his young sons.

Eddie Cibrian is being linked with LeAnn Rhimes while going through a break up with his wife.

"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 said 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," Cibrian said.

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.

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But

Cibrian

insisted: "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