WASHINGTON — The Supreme Court announced on Friday that it would enter the national debate over same-sex marriage, agreeing to hear a pair of cases challenging state and federal laws that define marriage to include only unions of a man and a woman.

One of the cases, from California, could establish or reject a constitutional right to same-sex marriage. Another case, from New York, challenges a federal law that requires the federal government to deny benefits to gay and lesbian couples married in states that allow such unions.