The New York Daily News said Fossella called it "an error in judgment."
The Republican congressman said in a statement: "As a parent, I know that taking even one drink of alcohol before getting behind the wheel of a car is wrong, I apologize to my family and the constituents of New York's 13th Congressional District for embarrassing them, as well as myself."
Fossella, 43, was arrested between midnight and 2 a.m., said Alexandria Police spokesman Lt. Ray Hazel. Fossella was charged with driving while intoxicated as a first offense, which under Virginia law requires a blood-alcohol level of 0.08% or higher, Hazel said
Back home, Democrat Steve Harrison, who is trying to unseat Fossella in the 13th District, said his foe should "seriously consider leaving Congress."
Said Harrison to the Daily News, "It's not an 'embarrassment,' it's a crime. He didn't admit anything. What the error in judgment is, he doesn't say," Harrison said.
Fossella - elected in November 1997 - is a member of the House Committee on Energy and Commerce. He is a former city councilman. His district includes all of Staten Island and the Brooklyn neighborhoods of Bay Ridge, Dyker Heights, Bensonhurst and Gravesend, according to the Daily News.