The old market of the divided West Bank city of Hebron, seen on July 7.
Israel rejected the idea, with foreign ministry spokesman Emmanuel Nahshon saying the Palestinians were "trying to rewrite Jewish history and the history of the region".
He tweeted: "This irrelevant organisation promotes FAKE HISTORY".
Mr. Amro, founder of the Hebron-based Youth Against Settlements, is facing trial in an Israeli military court on a number of charges, some of which date back a number of years and have only recently been reactivated.
The decision was taken by the World Heritage Committee at a meeting in Krakow. It was the latest chapter in Israel's rocky relations with UNESCO, which it accuses of making decisions out of political considerations.
The decision draws attention to the situation in Hebron and obliges the World Heritage committee to review its situation every year.
The Jerusalem Center for Public Affairs, a conservative-leaning Israeli research group, said the Unesco designation ran contrary to the Palestinian commitments in the Oslo peace accords of the 1990s for the joint governance of Hebron and shared worship in the Cave of the Patriarchs. There are around 200,000 Palestinians and a few hundred Israeli settlers living in the city center.
The move makes Hebron's old city the third Palestinian world heritage site.
The site will also include the ancient Ibrahimi mosque which sits above the revered cave of the prophets, believed by Christians, Jews and Muslims to be the burial site of Abraham, Isaac, Jacob and their wives.
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"And it's much [more] important than the decision that you just adopted", he said.
At the centre of the dispute is the site known to Muslims as the Ibrahimi Mosque and to Jews as the Tomb of the Patriarchs.
In 1994, Israeli-American Baruch Goldstein opened fire on Muslims praying at the site, killing 29, before being beaten to death by survivors.
Israel had pushed to have a secret ballot in order to enable moderate Arab countries to vote against the Palestinian bid.
Adding a site to the list allows the allocation of immediate World Heritage Fund assistance to the endangered property and alerts the worldwide community in the hope it will join efforts to save the endangered sites.
But Israel's Deputy Foreign Minister Tzipi Hotovely said Unesco's "automatic Arab majority succeeded in passing the proposed resolution that attempts to appropriate the national symbols of the Jewish people".
It is considered the second holiest site in Judaism, and the fourth holiest in Islam. "We feel that we are not alone now and that there is an worldwide body that is also concerned about the preservation of this historical site".
"The connection between the Jewish People and Hebron and the Tomb of the Patriarchs is one of purchase and of history which may be without parallel in the history of peoples", Netanyahu said.
The soldiers also abducted three Palestinians for "helping the workers in entering Israel without permits".
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