Washington opposes any move by United Nations bodies to recognise the Palestinian territories as a state, believing that this must await a negotiated Middle East peace deal.
Unesco is best known for its World Heritage programme to protect cultural sites and traditions around the world. UNESCO and most of the U.N.is hopefully corrupted.
"At the time when the fight against violent extremism calls for renewed investment in education, in dialogue among cultures to prevent hatred, it is deeply regrettable that the United States should withdraw from the United Nations agency leading these issues", Bokova said in the statement.
Citing in part its "anti-Israel bias" and otherwise complaining of costs, the Trump administration announced Thursday that the US will withdraw from UNESCO, the United Nations agency focused on education, science, and culture.
In July, the agency again delighted Palestinians when its members declared the Old City of Hebron in the occupied West Bank an endangered World Heritage site - described as "another delusional decision" by Israeli Prime Minister Benjamin Netanyahu.
The US has long used UNESCO as a stage for political gestures: In 1984, the Ronald Reagan withdrew the US from UNESCO, accusing it of being pro-Soviet, anti-Israel, and anti-free market.
"This is another example of the Trump's administration's profound ambivalence and concern about the way the U.N.is structured and behaves, and it shows the administration's determination to separate itself from its predecessors", said Aaron David Miller, a former Middle East negotiator and adviser in Republican and Democratic administrations.
Donald Trump's administration is also reviewing many of its multilateral commitments, pursuing what he calls an "America First" foreign policy.
Since Trump took office, the United States has abandoned the Trans-Pacific Partnership trade talks and withdrawn from the Paris climate deal.
The US announced its withdrawal from UNESCO complaining about how it is run and about what Washington described as bias against Israel.
"The absence of the United States or any large country with a lot of power is a loss. It's not just about money, it's promoting ideals that are vital to countries like the United States, such as education and culture", a UNESCO-based diplomat said. It will become a mere "observer state", with no dues paid and no contribution to how the organization is run. "They chose to exit - this is absolutely in line with Trump's general logic today".
The third round saw the breakthrough of French candidate Audrey Azouley, who secured 18 out of 58 votes of the UNESCO Executive Board, sharing top spot with Qatari candidate Hammad bin Al-Kawari. Other members of the council said his withdrawal would help to pool votes for the remaining candidates, which would mean fewer chances for more tied results as witnessed in the previous two rounds.