The Obama administration will give same-sex couples who are legally married the same status as other married couples in federal legal matters—including bankruptcy proceedings, prisoner visitation and death benefits for slain police officers, Attorney General Eric Holder said Saturday.

The Justice Department, Mr. Holder said, would issue new instructions to its employees on Monday to extend the same protections historically afforded to heterosexual married couples. He made the announcement at a speech in New York to the Human...