"We are examining whether this is a nationalistic stabbing, but other leads are being examined as well," police spokesman Micky Rosenfeld said, using Israel's term for an attack by Palestinian militants.
Kaye Wilson, a Briton who immigrated to Israel, said she and Christine Logan, a visitor from the United States, were attacked by two Arab men while hiking on Saturday south of Jerusalem in an area near Israel's border with the occupied West Bank.
"All of a sudden two Arabs walked by and they asked me in Hebrew if I had any water. So I said, dismissively, 'see ya'. But I immediately felt that something was wrong," Wilson told Israel's Channel Two TV from her hospital bed.
"I was scared, but my friend became a bit hysterical, so I told her in English -- they spoke in Arabic -- 'be quiet, don't make any noise, it'll make them attack us,'" she said.
"Suddenly, they came, it happened so quickly. They attacked us. One of them took out a very long knife, not a bread knife, but one that was serrated," Wilson said.
"I played dead. I saw (the knife) hadn't gone into my heart. My friend was dying, I heard her making gurgling sounds."
Wilson, who was stabbed several times, managed to reach a parking area where people called the police, who mounted an overnight search for Logan. Her bound body was found early on Sunday.
Police identified Logan as an American but gave no hometown.
(Additional reporting by Maayan Lubell; Editing by Janet Lawrence)