Madonna, who was raised Catholic, has in recent years publicly embraced the teachings of Kabbalah, a form of Jewish mysticism. She traveled to Israel Wednesday, the eve of the Jewish new year, to attend a conference on Kabbalah.
She exchanged gifts with Peres at his Jerusalem home Saturday.
Peres bestowed upon Madonna a lavishly bound copy of the Jewish Bible, while the singer gave Peres a copy of "The Book of Splendor," the guiding text of Kabbalah, Usmagazine.com said.
Inside the volume, she wrote, "To Shimon Peres, the man I admire and love, Madonna," the Yediot Ahronot daily reported.
"You don't know how popular the Book of Splendor is among Hollywood actors," Madonna reportedly told Peres. "Everyone I meet talks to me only about that. I am an ambassador for Judaism."