Palestinian men armed with knives and a gun killed at least three people and wounded several others in a string of attacks in Jerusalem and near Tel Aviv on Tuesday, police said, on a "Day of Rage" declared by Palestinian groups.

With the worst unrest in years in Israel and the Palestinian territories showing no sign of abating, Prime Minister Benjamin Netanyahu convened an emergency meeting of his security cabinet to discuss what police said would be new operational plans.

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Officials said Israel was considering whether to seal off Palestinian districts in East Jerusalem - home of many of the assailants of the past two weeks - from the rest of the city.

Unlike their brethren in the occupied West Bank, East Jerusalem Palestinians can travel freely in Israel. It annexed East Jerusalem after a 1967 war in a move not recognized abroad.

In Jerusalem, two Palestinians shot and stabbed passengers on a bus, killing two and injuring four, police said. One of the assailants was killed and the other captured.

Minutes later, a Palestinian rammed his car into a bus stop in an ultra-Orthodox Jewish neighborhood of the city, police said. A surveillance video showed him then hacking pedestrians with a cleaver until he was shot dead by a passer-by. One of the Israelis he attacked died and six others were hurt, police said.

In clashes near the West Bank city of Bethlehem, the Israeli army shot dead a Palestinian, medics said. The army said its troops fired on a man who tried to throw a petrol bomb at them.

Seven Israelis and 29 Palestinians, including 10 alleged attackers and eight children, have died in the surge of violence. The Obama administration, whose efforts to broker an Israeli-Palestinian peace deal stalled last year, voiced alarm.

"The United States condemns in the strongest terms today’s terrorist attacks against Israeli civilians," State Department spokesman John Kirby said, adding that Washington urged both sides "to prevent actions that would further escalate tensions".