The religious site in Jerusalem's Old City is one of the most sensitive issues in peace negotiations between Israel and the Palestinians, and the comments by Rabbi Israel Meir Lau could intensify the debate.
The Muslims call the site the Noble Sanctuary, the third holiest site in Islam. The two mosques in the compound are built atop the ruins of the two Jewish biblical temples, the holiest site in Judaism.
In a message to Prime Minister Ehud Barak, Lau said Muslim authorities were systematically destroying archeological remains from the temples, Lau's spokesman Itzik Rath said Tuesday.
After Israel captured east Jerusalem in the 1967 Mideast War, Israeli Defense Minister Moshe Dayan ordered that the keys to the Temple Mount be returned to the Muslims. He feared Israeli control could provoke a religious war with the entire Muslim world.
But Lau said Dayan made a terrible mistake.
``Handing over the keys of the Temple Mount to the Waqf was a major historic mistake over which generations will weep,'' Lau said in his message to Barak.
Most rabbis say Jews must not visit the site due to problems connected with ritual purity, but Jews still regard the entire compound as sacred and pray outside its Western Wall, a remnant of the second Temple.
Israel claims sovereignty over the site, while the Muslims maintain day-to-day control.
The Palestinians are demanding sovereignty over the entire compound, but Barak says he will never grant this to the Palestinians. He has not ruled out handing over sovereignty to a third party.
Successive Israeli governments have been unwilling to press Israel's sovereignty on the Temple Mount and ensure archeological supervision of the Muslim Trust, the Waqf, which runs the compound.
Both the Waqf and the Israeli police have denied recent reports that the Wakf was digging a tunnel from the basement of the Al-Aqsa mosque to a hall known as Solomon's Stables.
The senior Muslim cleric of Jerusalem, Ikrim Sabri, denies that the Jewish temples ever existed and says the Jews have no connection with the place or with Jerusalem.