Egyptian candidate Khattab received 12 votes, while Hamad bin Abdul Aziz Al-Kawari of Qatar ended up with 20 votes, Audrey Azoulay from France with 13 votes, Pham Sanh Chau of Vietnam with five votes, Qian Tang from China with five votes, and Vera El Khoury Lacoeuilhe from Lebanon with three votes.
China's announcement also followed the decision by the United States and Israel to pull out of the UN Educational, Scientific and Cultural Organisation (UNESCO) in protest at its alleged "anti-Israel bias".
Thirty votes are needed to clinch the nomination to head the Paris-based UN Educational, Scientific and Cultural Organization.
Egypt's candidate for the post of Director-General of UNESCO, Moushira Khattab, lost the runoff vote to her French rival, who will run the final round against the Qatari candidate on Friday.
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The body's 58 board members have been gathered in the French capital selecting a candidate since Friday.
The victor must be approved by UNESCO's 195 member states in November, though this is seen as a formality.
The final vote between Azoulay and Al-Kawari will take place later on Friday, with a toss in case of a tie.
Most of the candidates acknowledge the need to reform the 71-year-old organisation whose bloated bureaucracy is accused of inefficiency.
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China was silent on its reported decision to withdraw its candidate from the race for UNESCO's Director-General.
This is not the first time the USA, a founding member, has walked out on the 195-member Unesco, best known for producing a list of World Heritage sites including tourist favourites such as the Grand Canyon or Cambodia's Angkor Wat.
But in 2011 relations soured again after UNESCO admitted Palestine as a full member, prompting the U.S. to cut its funding to the organisation, leaving a gaping hole in its finances.
However, UNESCO does not observe the kind of rotation by world region which is used when choosing a UN secretary general.
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