She called the US departure a loss for "the United Nations family" and for multilateralism, saying the USA and UNESCO matter to each other more than ever now to better fight "the rise of violent extremism and terrorism".
In 2011 the United States cut its funding to the agency - slashing its budget by 22 percent - in protest at its decision to grant full membership to the Palestine.
A US State Department statement said the decision to withdraw reflected "concerns with mounting arrears at UNESCO, the need for fundamental reform in the organization, and continuing anti-Israel bias at UNESCO". It cited US belief in "the need for fundamental reform in the organization".
Netanyahu called the United States withdrawal "brave and moral", adding that UNESCO, "distorts" history instead of preserving it.
In October 2016, Israel suspended its ties with UNESCO after the organization voted in favor of a resolution that warns over the escalating violence around the holy site in East Jerusalem, a territory that Israel seized in 1967 and annexed shortly later.
Hours after the USA announced its withdrawal, the Israel joined in, with Prime Minister Benjamin Netanyahu saying he had instructed his foreign ministry to begin preparations to leave.
The United States has walked away once before under ex-president Ronald Reagan, who quit UNESCO in 1984 over alleged financial mismanagement and claims of anti-US bias in some of its policies.
US officials said Secretary of State Rex Tillerson made the decision and it was not discussed with other countries. With no funds forthcoming, the US lost its vote in the agency in 2013.
Many saw the 2011 UNESCO vote to include Palestine as evidence of long-running, ingrained anti-Israel bias within the United Nations, where Israel and its allies are far outnumbered by Arab countries and their supporters.
UNESCO, which is best known for producing the list of World Heritage sites that includes the Grand Canyon and other USA attractions, has been the scene of diplomatic flare-ups in recent years after Arab countries succeeded in passing a number of resolutions critical of Israel. Unesco was dependent on the United States for 22 percent of its budget, then about $70 million a year.
Michael Worbs, chairman of the UNESCO Executive Board, appreciated the Vietnamese' notable jump in the second round.
In the run-up to selecting a candidate for the director-general position of UNESCO, most countries will pull out of the race if their candidate fails to secure 10 or more votes in two rounds.
But according to Nikki Haley, the US ambassador to the United Nations, the Trump administration found it to be a step too far when the agency decided this summer to designate "the Old City of Hebron and the Tomb of the Patriarchs as part of Palestinian territory".
That year the U.S. stopped paying into UNESCO but did not officially withdraw.
The Director General gave examples of collaborating during that time, such as launching the Global Partnership for Girls' and Women's Education and celebrating World Press Freedom Day in Washington, D.C., with the National Endowment for Democracy.
The US was a founding member of UNESCO.