The UNESCO resolution referred to the holy site in Jerusalem's Old City only by its Muslim name, Al-Aqsa or Al-Haram al-Sharif.
Palestinians say the Israeli measures are aimed at paving the way for the Judaization of the city.
The UNESCO resolution, tabled by several Arab countries and approved on Tuesday, calls on Israel, as the "occupying Power", to cease "persistent excavations, tunneling, works and projects in East Jerusalem", which the Palestinians want as the capital of their future state.
"Once again UNESCO member states tried to deny the historical connection of the Jewish people to Israel", he told the Washington Examiner.
In a marked change from the near unanimous approval seen in similar UNESCO votes on Jerusalem, 23 member states abstained and 10 - the US, Italy, the United Kingdom, the Netherlands, Lithuania, Greece, Paraguay, Ukraine, Togo and Germany - opposed.
The resolution, a document seen by Reuters TV, said it aimed to "safeguard the cultural heritage of Palestine and the distinctive character of East Jerusalem" and reaffirmed that all legal and administrative decisions taken by Israel concerning the status of the Holy City were "null and void and must be rescinded forthwith".
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The UNESCO resolution further ignores that the Temple Mount and Western Wall - the holiest sites in Judaism - are located in eastern Jerusalem, which is steeped in Jewish history.
The United Nations' cultural agency voted to condemn Israel's sovereignty in Jerusalem. Israel has long complained of bias at U.N. forums, feeling outnumbered by Arab nations and their supporters.
The resolution, submitted by several Arab nations, has softer wording than another UNESCO decision past year that referred to several sites primarily by their Islamic names and largely ignored Jewish terms.
"Under President Trump, if the world knows nothing else, the world will know this - America stands with Israel", Pence said to applause.
Italian Foreign Minister Angelino Alfano said he had instructed the country's representative to UNESCO to vote against "the latest politicized resolution on Jerusalem". "Our opinion is very clear - UNESCO can not become the venue for a permanent ideological clash to address issues that other bodies are delegated to solve".
He, however, noted that "since the Palestinian Authority would like to make East Jerusalem the capital of an eventual state, picking Jerusalem as the site of an embassy would be a clear signal that a country favours one side over the other".