A spokesman for Interior Minister Eli Yishai said he was not prepared to give up Israeli sovereignty, "even if it is only symbolic," Haaretz reported Monday.
Tourism Minister Stas Misezhnikov questioned the proposal from Peres, saying there are no guarantees such a "great gift" would increase tourism by Christian pilgrims, Haaretz reported.
"If we were sure that this great gift to the Christian world would bring millions of Christian pilgrims here, then we would have a good reason to think about (agreeing to the demand)," Misezhnikov said. "But since we are not certain that this will happen, why should we hand out gifts?"
The issue has resurfaced as Israel prepares for a visit from Pope Benedict XVI next week. The Vatican has requested sovereignty over six sites in Israel including the Church of the Annunciation in Nazareth, Mount Tabor and Jerusalem's Coenaculum on Mount Zion, the reported location of Jesus Christ's Last Supper.
The Jerusalem Post said the remaining Christian sites in Israel being sought by the Vatican are the Gethsemane on the Mount of Olives in Jerusalem and the Church of the Multiplication.
Notable deaths of 2014 [PHOTOS]