"The director general has received death threats and her protection has had to be reinforced," Carmel Shama Cohen said on Israeli public radio.
"These threats were made after her criticism" of two resolutions adopted last week at committee stage ahead of a final vote, Cohen said, accusing Arab countries of "appalling conduct" over the drafts.
Bokova distanced herself from the resolutions in a statement, saying "nowhere more than in Jerusalem do Jewish, Christian and Muslim heritage and traditions share space".
They refer to the Al-Aqsa mosque compound in east Jerusalem's Old City -- Islam's third holiest site -- without any reference to the site also being revered by Jews as the Temple Mount.
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Israel suspended cooperation with UNESCO on Friday, a day after its committee adopted the two resolutions, which the Jewish state said ignored "thousands of years of Jewish ties to Jerusalem".
The two resolutions are due to be put to the executive board of the United Nations Educational, Scientific and Cultural Organization on Tuesday, which generally votes with the line taken by committees.
The status of Jerusalem is the thorniest issue of the Israel-Palestinian conflict.
Israel captured east Jerusalem during the 1967 Middle East war and later annexed it in a move not recognised by the international community, declaring the entire city to be its indivisible capital.
The Palestinians see east Jerusalem as the capital of their promised future state.
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