Behind them in the secret ballot was Egyptian career diplomat Moushira Khattab with 13 votes and China's Tang Qian with five, according to results posted on UNESCO's website. The United States is pulling out of UNESCO because of what Washington sees as its anti-Israel bias and a need for "fundamental reform" of the U.N. cultural agency.
The election of UNESCO's new chief has been narrowed down to two candidates, one from Qatar and the other from France.
Egypt's candidate passed on Thursday the third round of the organization's election held in Paris, France, where no candidate gained an absolute majority of votes so far.
Both countries suspended their funding to the agency - best-known for its prestigious World Heritage List - over the move.
The last round of balloting, at institution's headquarters in Paris, would be representative of Qatar, Hamad Al-Kawari, to French Audrey Azoulay.
Jewish groups have taken issue with Al-Kawari's candidacy, citing a preface the former Qatari Culture Minister wrote to a 2013 Arabic book called "Jerusalem in the Eyes of the Poets" that they accuse of anti-Semitism.
French Jewish candidate Audrey Azoulay beat out her Egyptian competition for the right to compete in the final round of voting for the position of UNESCO director-general on Friday evening.
The body's 58 board members have been gathered in the French capital selecting a candidate since Friday.
The proceedings have been overshadowed by the USA decision, announced Thursday, to withdraw from the agency.
UNESCO has been accused of bias in the Israeli-Palestinian conflict, and it infuriated Israel and staunch ally the United States by granting full membership to Palestine in 2011.
UNESCO's general assembly will have to sign off on the board's pick.