Qatar's Hamad bin Abdulaziz al-Kawari and France's Audrey Azoulay -- both former culture ministers -- had 18 votes apiece in the battle to replace outgoing UNESCO director-general Irina Bokova.
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.
Vera El Khoury of Lebanon came last on four votes.
Thirty votes are needed to clinch the nomination to head the Paris-based UN Educational, Scientific and Cultural Organization.
The body's 58 board members have been gathered in the French capital since Friday selecting a candidate.
The winner must be approved by UNESCO's 195 member states in November, though this is seen as a formality.
Vietnam's Pham Sanh Chau dropped out of the race Wednesday, having scored five votes in the second round. Candidates from Guatemala, Iraq and Azerbaijan have also given up.
If no candidate wins an outright majority after Thursday's fourth round, it goes to a run-off between the top two.
Most of the candidates acknowledge the need to reform the 71-year-old organisation whose bloated bureaucracy is accused of inefficiency.
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.
Both countries suspended their funding to the agency -- best-known for its prestigious World Heritage List -- over the move.
Arab countries have complained that UNESCO has never had a boss from their region.
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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