Four US citizens were kidnapped by armed men on 3 March while driving into the city of Matamoros in the north-eastern state of Tamaulipas, Mexico, across the border from Texas.
BBC reports they had travelled there for cosmetic surgery, relatives told US media.
One man, named only as José "N", 24, from Tamaulipas, has been arrested.
White House National Security Council spokesman John Kirby said: "We offer our deepest condolences to the friends and families of those who were killed in these attacks."
