Bush-era Surgeon General Richard Carmona announced today he is running in Arizona’s open-seat Senate race, handing national Democrats a recruiting victory in a contest that could be competitive next year.

“After talking with my family, my friends, and fellow Arizonans, I have decided to run for the United States Senate,” he said in an email statement.

According to published reports, among those who encouraged him to run is President Barack Obama. National Democrats have been touting Carmona to reporters in recent weeks.

Possibly looking to neutralize his record in a Republican administration, he wrote in his announcement statement: “As Surgeon General my job was to be the doctor to every American — not to one political party.”

Carmona’s entrance sets up a contested Democratic primary. Former state Democratic Chairman Don Bivens is also running. Earlier this week he picked up an endorsement from former Rep. Ann Kirkpatrick, who is seeking a comeback in 2012.

Roll Call currently rates the Arizona Senate race as Likely Republican.