The six candidates who made it to the vote were Moushira Khattab (Egypt), Audrey Azoulay (France), Polad Bülbüloglu (Azerbaijan), Juan Alfonso Fuentes Soria (Guatemala), Pham Sanh Chau (Vietnam), Qian Tang (China), and former Qatari Minister of Culture Hamad Abdul Aziz al-Kawari, who is now the cultural affairs adviser to the Emir of Qatar.
No results were achieved in third stage of voting to elect UNESCO director general, TASS reported.
UNESCO's general assembly will have to sign off on the board's pick next month, but it's seen as a formality.
Azoulay received 31 votes, compared to 25 for Egyptian human rights activist Moushira Khattab.
The ministry said the request made Friday was submitted by Egypt's permanent mission to UNESCO.More news: Wells Fargo $1 billion accrual due to talks with US Justice Department
Azoulay will now face off against Qatar's Hamad Al-Kawari in a vote due to be held at 6:00 pm (1600 GMT).
The victor to be selected on Friday will succeed outgoing Director-General Irina Bokova, whose 8-year term leading the United Nations cultural agency was marred by financial woes and criticism over Palestine's inclusion as a member.
The rift continued to fester in recent years, with the organisation becoming the scene of repeated diplomatic flare-ups after efforts led by Arab countries to pass resolutions critical of Israel.
Under these circumstances, our candidacy for the post of Director-General of UNESCO takes on a new significance.
Egyptian Foreign Minister Sameh Shoukry, who was in Paris for the vote, "urged all his friends to vote for France" instead of Qatar in the final round, a member of Khattab's delegation told AFP. If no candidate gets the 30 votes needed, the top two candidates will go into a run-off.