WASHINGTON  The Justice Department has decided that federal prosecutors should enforce criminal provisions in the Violence Against Women Act in cases involving gay and lesbian relationships, a newly disclosed memorandum shows.

In a seven-page legal analysis, David J. Barron, the acting assistant attorney general of the Justice Department’s Office of Legal Counsel, concluded that federal prosecutors may use the law in cases of interstate stalking and domestic violence regardless of whether the victim or the defendant is a man or a woman.

“The text, relevant case law and legislative history all support the conclusion” that the law’s criminal provisions “apply when the offender and the victim are the same sex,” Mr. Barron wrote.

The memorandum was addressed to the acting deputy attorney general, Gary Grindler, who had apparently asked the Office of Legal Counsel to consider the question. The document was posted on the Justice Department’s Web site on Wednesday.