The violence was another challenge to US efforts to revive Middle East peace talks after Israel angered Palestinians and touched off a dispute with Washington by announcing a Jewish settlement project near East Jerusalem, an area captured along with the West Bank in a 1967 war.
In a deepening US-Israeli crisis, US Middle East envoy George Mitchell canceled plans to return to the region on Tuesday after Prime Minister Benjamin Netanyahu said he would not curb such construction, opposed by the United States.
Clashes erupted in several areas of East Jerusalem.
Palestinians hurled stones at police and burned tires and trash bins. Police responded with tear gas and fired rubber bullets.
Some 40 Palestinians were treated at East Jerusalem hospitals for minor injuries and two policemen were hurt, medical officials said.
A police spokesman said some 3,000 officers were put on high alert after Hamas, which controls the Gaza Strip and wields influence in the West Bank and East Jerusalem, urged Palestinians to mount anti-Israeli protests.
"We call on the Palestinian people to regard Tuesday as a day of rage against the occupation's (Israel's) procedures in Jerusalem against Al-Aqsa mosque," Hamas said in a statement.
Hamas leaders said renovation of the Hurva synagogue, in the Jewish Quarter of Jerusalem's walled Old City, was an Israeli plot to demolish Al-Aqsa Mosque, some 400 meters away.
Israel, they said, wanted to build a Jewish temple to replace Al-Aqsa, the third holiest mosque for Muslims.
Israel has denied the allegation and the US State Department, appealing for calm, voiced concern at what it described as Palestinian incitement and mischaracterization of the restoration work.
An inauguration ceremony was held on Monday at the synagogue, which was blown up in the 1948 Middle East war. Israel captured the area 19 years later.
Sporadic violence has erupted in recent weeks in Jerusalem after Israel decided to include West Bank religious sites in a Jewish national heritage plan stoked Palestinian anger.
Citing biblical and historical links, Israel sees all of Jerusalem as its capital, a claim not recognized internationally. The Palestinians want East Jerusalem to be the capital of a future state in the West Bank and Gaza Strip.
Israel's announcement, during a visit last week by US Vice President Joe Biden, of the plan to build 1,600 homes for Jews near East Jerusalem embarrassed the White House. The Palestinians, who had just agreed to begin indirect talks with Israel, demanded the project be scrapped first.
US Secretary of State Hillary Clinton, in unusually blunt remarks, called Israel's actions an insult. Netanyahu voiced regret at the timing of the move but made no move to cancel the plan. Israel said construction was several years away.
Clinton telephoned Netanyahu on Friday to convey unspecified demands about the housing project as well as about demonstrating commitment to the US-mediated peace talks, the State Department said, without elaborating.
US officials said they were still waiting for Israel's formal response. Israeli media reports said Clinton had asked for the settlement plan to be scrapped and for Israel to agree to discuss core statehood issues with the Palestinians.
