The caller, who reached the police emergency line, was reportedly a man with a native Hebrew accent.
Meanwhile, police Inspector-General Assaf Hefetz has ordered an investigation into the sources and distribution of a new bumpersticker: "Shalom Haver 2" (Goodbye Friend 2).
The sticker is made out in the same form and print as the original sticker with the two words coined by President Bill Clinton, which became the most prevalent slogan after prime minister Yitzhak Rabin's assassination.
Histadrut chairman Amir Peretz, in seeking the police probe, called the sticker "chilling"
"Even if the explicit name does not appear on it," he said, "the threat against Peres is obvious."