The Israeli military said one of its soldiers was lightly wounded during the scuffles. There were no reports of any Palestinians wounded.
Israeli Prime Minister Benjamin Netanyahu sparked anger on Sunday when he said he hoped to include the Tomb of the Patriarchs in Hebron and Rachel's Tomb in Bethlehem in a 100-million-dollar plan to restore national heritage sites.
"We strongly condemn this decision which yet again confirms the Israeli government's determination to impose facts on the ground," chief Palestinian negotiator Saeb Erakat told AFP.
"This Israeli decision is provocative for Muslims around the world and especially Palestinians," he said.
The Islamist Hamas movement ruling the Gaza Strip also lashed out at the decision, with its tourism minister Mohammed al-Agha calling on Palestinians in Israel and the West Bank to make their way to the site and "defend" it.
Egypt and Jordan, the two Arab countries to have signed peace treaties with Israel, denounced the Israeli decision.
"The decision is illegal," Egyptian foreign ministry spokesman Hossam Zaki said in a statement. "This new Israeli position will only feed extremism, confrontations and violence, and it does not serve US efforts to revive peace."
Jordan condemned what it called Israel's "provocative" plan to include the sites, saying it would "harm peace efforts in the region and anger millions of Muslims around the world."
The Tomb of the Patriarchs in Hebron, where the biblical figure Abraham is believed to be buried, is sacred to both Muslims and Jews and has long been the scene of tensions.
A few hundred hardline Jewish settlers under heavy Israeli military protection have taken up residence near the site and converted part of the Ibrahimi mosque above it into a synagogue.
The mosque was the site of the infamous massacre of 29 Palestinian worshippers in 1994 by Jewish extremist Baruch Goldstein, who was beaten to death by survivors during the melee that followed the shooting.
More than 160,000 Palestinians live in Hebron, from which the Israeli military partially withdrew in 1998.
The tomb of the Jewish matriarch Rachel is in an Israeli enclave in the West Bank town of Bethlehem surrounded by eight-metre- (24-foot) high concrete walls.
Israel's last-minute decision to include the two sites in the announcement of the plan followed protests from right-wing ministers. A government spokesman insisted on Sunday the list of some 150 sites was not final.
UN Middle East envoy Robert Serry expressed concern about the Israeli plans and the resulting "heightened tensions."
"These sites are in occupied Palestinian territory," he said in a statement. "I urge Israel not to take any steps on the ground which undermine trust or could prejudice negotiations."
Peace talks have been suspended for more than a year over the issue of settlement construction in the occupied West Bank, including mostly Arab east Jerusalem, annexed by Israel in 1967 in a move not recognised internationally.
The Palestinians have demanded a full settlement freeze before returning to negotiations, but Israel has agreed only to a temporary easing of growth that excludes east Jerusalem, which the Palestinians view as their future capital.
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