Leahy filed the amendment on Tuesday, the same day the Senate approved a motion to proceed on the Border Security, Economic Opportunity and Immigration Modernization Act.

The amendment gives equal protection to immigrants who are in same-sex marriages. Specifically, the amendment makes the immigration bill recognize "any marriage entered into full compliance with the laws of the State or foreign country within which such marriage was performed."

The amendment changes the text of the bill so it reads "his or her spouse" instead of "his spouse" and strikes "husband and wife" and replaces that with "the spouses."

"Seeking equal protection under our laws for the LGBT [lesbian, gay, bisexual, transgender] community, is the right thing to do," Leahy said. "I withheld my anti-discrimination amendment during the Senate Judiciary Committee markup. As the entire Senate turns to debate the immigration bill, the fight for equality must go on."

The Senate voted 84-15 to proceed to the immigration bill on Tuesday afternoon.