Azoulay will now face off against Qatar's Hamad Al-Kawari in a vote due to be held at 6:00 pm (1600 GMT).
Spokesperson Hua Chunying made the remarks when asked to comment on the decisions of the USA and Israel to withdraw from the United Nations Educational, Scientific and Cultural Organisation (UNESCO).
Khattab came third in the ballot after Qatar's Hamad al Kawari and France's Audrey Azoulay, who won 20 and 13 votes respectively.
Azoulay succeeds outgoing Director-General Irina Bokova of Bulgaria, whose eight-year term was marred by financial woes and criticism over Palestine's inclusion as a member. "Audrey!" following her victory and said the response to UNESCO's problems was to reform the agency, not to walk away - an understated rebuke of the USA and Israel.
Arab countries have complained that UNESCO has never had a boss from their region.
UNESCO's general assembly will have to sign off on the board's pick next month, but it's seen as a formality.
Al-Kuwari topped the voting and qualified for the final round.
The new director will set priorities for the organization best known for its World Heritage program to protect cultural sites and traditions.
Arab countries have long wanted to lead the organization, but the Palestine issue has complicated the election.
The two went on to say that UNESCO's Executive Board "appears to be squandering the chance to put those ideals and values ahead of base political considerations", and urged members to vote for an alternative candidate.
The victor must be confirmed by the UNESCO general conference next month and will replace outgoing Director-General Irina Bokova in January 2018.
In addition, the UNESCO vote comes as Egypt and three other Arab nations continue a months-long boycott of Qatar over allegations that the government funds extremists and has overly warm ties to Iran.
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.