Arab diplomats say that the American position is a bit disingenuous, since Washington has maneuvered to try to prevent the Palestinians from getting the necessary 9 votes in the 15-seat Security Council, and would use its veto there if they did. The announcement on Monday by Bosnia, which currently has a seat on the Council, that it would abstain appeared to deny the Palestinians the chance for nine yes votes, making an American veto appear unnecessary.

At Unesco, though, no country has a veto.

Mr. Killion said in a statement that “there are no shortcuts” to a Palestinian state and that “we believe efforts such as the one we have witnessed today are counterproductive.” Last week, Secretary of State Hillary Rodham Clinton called the Unesco application “inexplicable.”

Both parties in Congress denounced the Unesco action on Monday. Representative Nita M. Lowey, Democrat of New York, called it “counterproductive,” saying in a statement that “Unesco is interfering with the prospects for direct negotiations between Israel and the Palestinians.” Ileana Ros-Lehtinen, the Florida Republican who heads the House Foreign Affairs Committee, characterized the Unesco move as “anti-Israeli and anti-peace” and called for a quick cutoff of funds.

There has been some discussion of Arab nations contributing more to Unesco to make up the budget shortfall, but nothing has been promised. And the Unesco bylaws seem to require that extra funds contributed to the group cannot be used for its operating budget.

Ms. Bokova, the Unesco director general, said in interviews that she was concerned about immediate financial problems for her agency, and about American disengagement, which she said ran counter to the United States’ “core security interests” and which she hoped would be temporary. After the vote, she said that she was worried that “the universality and financial stability” of Unesco would be jeopardized.

The Israeli ambassador, Nimrod Barkan, said that Unesco had done “a great disservice” to international efforts to restart negotiations between Israel and the Palestinians. “Unesco deals in science, not in science fiction,” he said, noting that a Palestinian state is not otherwise recognized by the international community. Unesco, he said, had acted on a “political subject outside of its competence.”