Palestinian President Mahmoud Abbas called Tuesday for calm after several weeks of heightened unrest with Israel, saying his people had no interest in any further "escalation" and urging renewed dialogue.

The comments marked the Palestinian leader's strongest attempt yet to restore calm after the worst outbreak of fighting in months, and came as Israeli Prime Minister Benjamin Netanyahu vowed to take even tougher measures to quell the violence.

The clashes erupted three weeks ago at the start of the Jewish new year and have turned more violent in recent days. Four Israelis were killed last week in shooting and stabbing attacks in Jerusalem and the West Bank, while Israeli forces have killed four Palestinians, including a 13-year-old boy, amid violent protests.

Both Abbas and Netanyahu are dealing with precarious domestic situations as they try to find a way out of the crisis.

Netanyahu is under heavy pressure, particularly from hard-liners in his governing coalition, to respond with a tough crackdown. Abbas, fed up with years of diplomatic paralysis and unpopular with his public, does not want to appear to be caving in to Israeli pressure. Yet neither man has an interest in seeing the violence spin out of control.

Speaking to senior officials of the Palestine Liberation Organization in the West Bank city of Ramallah, Abbas said he has told the Israelis that the Palestinians don't want "military and security escalations." He said the message had been delivered to Palestinian security forces and activists but added that, "at the same time, we will protect ourselves."

Abbas also said he was ready to renew dialogue with Israel, a topic that could come up during a gathering of international Mideast envoys from the U.S., Europe, Russia and the United Nations in Jerusalem on Oct. 14.

Clashes took place in several places across the West Bank on Tuesday.

In Qalandia, on the outskirts of Jerusalem, demonstrators hurled burning tires, rocks and a firebomb at Israeli forces, injuring one riot police officer, the Israeli military said. It said troops opened fire with rubber bullets and small .22-caliber rounds, shooting demonstrators in the legs. Clashes also erupted in the West Bank cities of Bethlehem, Nablus, Ramallah, Jenin and Hebron.

The Palestinian Red Crescent medical service said 39 people were wounded, including a 17-year-old boy who was in serious condition after being shot in the abdomen.

Israeli police said a crowd of demonstrators in Jaffa, a largely Arab area of Tel Aviv, clashed with police Tuesday night, throwing rocks at cars and police officers, injuring two officers.

But in a sign that things might be calming, there were no major incidents of violence in Jerusalem, police said.

In New York, U.N. Secretary-General Ban Ki-moon's office said he was "profoundly alarmed" by the violence and called for "urgent action" by both sides to ease tensions.

Israel has already beefed up its forces in Jerusalem and the West Bank in recent weeks and is under intense domestic pressure to do more. Thousands of Israelis, including three Cabinet ministers in his own party, demonstrated outside the prime minister's residence on Monday night, demanding tough action.

On Tuesday, Netanyahu visited the site of a West Bank shooting where an Israeli settler and his wife were killed last week as they were driving and promised additional measures "to break this wave of terror like we broke previous waves of terror."

Speaking at a nearby army base, he instructed the military to "change the way of thinking" about Palestinian attackers and said Israel will deploy ground and aerial cameras along major West Bank roads to help prevent further such attacks.

Netanyahu also alluded to recent criticism from West Bank settler leaders and their allies that he is not doing enough to guarantee their security.

"Leadership is needed from public leaders, including the settler movement, maybe first and foremost with the settler movement," Netanyahu said. "We are in a continuing battle. Such a battle does not need a fiery reaction. It needs a lot of strength, a lot of tenacity, a lot of restraint."

In an initial move, the Israeli military demolished the homes of two Palestinian militants in east Jerusalem.

The destroyed homes belonged to the families of a man who killed four worshippers and a police officer in a Jerusalem synagogue last year, and a second attacker who killed one person when he rammed a bulldozer into traffic. Although the attackers were immediately killed, Israel often carries out such demolitions of the homes of militants' families, believing it will deter future attacks.

Also Tuesday, troops sealed off a room at the home of a third attacker, who tried to kill a prominent Orthodox Jewish activist last year, ahead of its potential demolition.

"If Netanyahu thinks that this will create deterrence, then he is wrong. This will not deter anybody," said Odai Hijazi, whose brother Motaz shot and seriously wounded Yehuda Glick, a Jewish nationalist who has campaigned for greater Jewish access to a sensitive Jerusalem holy site.

That site has been at the heart of the recent tensions. The hilltop compound is revered by Muslims as the spot where Prophet Muhammad ascended to heaven and by Jews as the site of the two Jewish biblical Temples. There have been several days of clashes at the site over the past few weeks as Palestinians barricaded themselves inside the Al-Aqsa mosque while hurling stones, firebombs and fireworks at police.

The unrest later spread to Arab neighborhoods of east Jerusalem and to the West Bank.

Many Palestinians believe that Israel is trying to expand a Jewish presence at the site. Netanyahu denies the claims, describing them as slander aimed at inciting Arabs to violence. On Tuesday, Netanyahu accused Israel's own Islamic Movement, a group that runs education and religious services for Israeli Arabs, of leading the incitement.