Mahmoud Al-Habbash, the Palestinian minister of endowments and religious affairs, said the move was "a way of showing solidarity with the people of Hebron."
Al-Habbash told Arab News his government was “trying to send the message that it is concerned and wants to protest the Israeli decision."
Israel’s decision last week drew widespread international criticism and heightened Palestinian suspicions of Israel at a time when the US is trying to restart peace talks.
Israelis and Palestinians have clashed frequently in the past over two West Bank sites added to the heritage list: the Cave of the Patriarchs in Hebron and Rachel's Tomb in Bethlehem.
The city's brewing tensions were on sharp display on Monday, when a group of settler youths, some as young as 4 years old, threw rocks and cursed at Palestinians not far from the site.
Palestinian President Mahmoud Abbas denounced Israel's move as an “attack on the holy places,” and the Hamas movement called for a new uprising.
Israeli Prime Minister Benjamin Netanyahu said the decision was about preserving culture, and not connected to politics.
Over the past week, Palestinian stone-throwers have clashed almost daily with Israeli troops in Hebron, where 500 Jewish settlers live in heavily guarded enclaves amid 170,000 Palestinians.
The Cabinet session came a day after Israeli police forces dispersed masked Palestinian protesters at Al-Aqsa Mosque. And early Monday, gunmen opened fire at an Israeli security vehicle in the East Jerusalem neighborhood of Silwan, lightly injuring a security guard, police said.
Palestinians fear the decision is another sign that Netanyahu wants to hang on to significant parts of the West Bank, a territory they want for their future Palestinian state, along with Gaza and East Jerusalem.
Fayyad convened his Cabinet at the Hebron governor's office Monday, instead of its usual venue in the city of Ramallah. The ministers were greeted by a military honor guard.
Fayyad condemned Israel's decision on the holy sites but also appealed for calm.
“We are not going to be drawn into a cycle of violence,” Fayyad said. “We are fully determined, and we count on our people understanding fully well that the best response to this ... is to stay focused” on state-building.
The disputed site in Hebron is a 2,000-year-old fortress-like structure built where tradition says the Prophet Abraham (peace be upon him) is buried. Muslims call it the Ibrahimi Mosque.
Israel partitioned the shrine, keeping apart Muslims and Jews, after an Israeli settler gunned down 29 Muslim worshippers there in February 1994, before being bludgeoned to death.
Hebron Mayor Khaled Osaily said the city's Palestinians are deeply suspicious. “The settlers came here for one reason, they want to claim that this is Jewish heritage, and not only for the mosque, but for the whole city of Hebron,” he said.
Netanyahu's move has also drawn international criticism.
In Brussels, the EU's foreign policy chief, Catherine Ashton, called the Israeli move “detrimental to attempts to relaunch peace negotiations.”
Visiting US Sen. John Kerry told reporters in Jerusalem Monday that he understood the Israeli leader's desire to preserve a historical site. “But the timing and the manner of the announcement needs to be taken into account in the future,” Kerry said.
Kerry said he hoped the clashes would prove to be no more than a “hiccup” toward getting US-mediated peace talks back under way -- a process that could resume in the coming weeks.
Also Monday, a Palestinian fighter in the Gaza Strip was killed by an Israeli tank shell close to the border with Israel, medics said. The Israeli military had no immediate comment.
-- With input from agencies
