WASHINGTON, Dec. 3—The Justice Department asked Federal Court today to strike down provisions of Alabama's Constitution and laws that make it a crime for whites and Negroes to marry. It was the first such action taken by the Government.which make it a crime to issue such a license.

The suit, filed in Birming ham, Ala., and announced in Washington, asked the court to order state officials to permit the marriage of Sgt. Louis Voyer, a white soldier stationed at Fort McClellan, Ala., and Phyllis Bett, a black woman from Anniston.

The couple sought a marriage license Nov. 10, the depart ment's complaint said, but were denied it on the basis of the state's Constitution and laws,

Probate Judge C. Clyde Brit tain of Calhoun County, who denied the license, and the State of Alabama were named as defendants.