Hours after her arrival, Madonna visited the Western Wall and its ancient tunnel, officials said Monday.
The 51-year-old singer will perform concerts at Tel Aviv's Hayarkon Park Tuesday and Wednesday as part of her Sticky and Sweet Tour.
Madonna planned to meet with Livni and her husband for dinner Monday night and with Netanyahu Friday, the Yedioth Aharonoth newspaper said.
Madonna will also visit the graves of Talmudic sages in Safed, and attend a Kabbalah center event during her visit, the newspaper said.
A letter by Safed Rabbi Shmuel Eliahu published in Maariv Monday, asked Madonna to respect the city's holy sites and dress accordingly during her visit.
Madonna was accompanied by her boyfriend, Jesus Luz, and children Lourdes, Rocco John, David Banda and Mercy James, Yedioth said.
Campaigners for the release of kidnapped Israel soldier Gilad Shalit approached the Live Nation company, which represents Madonna, and asked if she would mention Shalit at her performances, Yedioth Aharonoth said. Company spokeswoman Susan Rosenberg rejected the request, saying Madonna does not involve herself in politics, the newspaper said.
However, concert producers told the newspaper the concert lineup stipulates the singer intends to make "political statements relevant to Israel" between songs, the report said.