Jerusalem suffered its bloodiest day yet in a recent wave of unrest, with at least three Israelis killed as Palestinian attackers shot at a bus and another rammed a car into pedestrians.
The bus attack on Tuesday was the first assault with a gun in Jerusalem in the two-week-old upsurge of Palestinian violence.
The rising tide of violence, which has seen a series of stabbing attacks and protests, has raised fears of a full-scale third Palestinian intifada, or uprising.
A Palestinian was also killed in clashes in the West Bank city of Bethlehem.
In the intifadas of 1987-1993 and 2000-2005, hundreds of people were killed in near daily Israel-Palestinian violence.
Prime Minister Benjamin Netanyahu said Israel would use "all means" available to end Palestinian violence.
Speaking to parliament, he warned Palestinian president Mahmud Abbas that he would hold him responsible if incitement led to a further deterioration.
Netanyahu's security cabinet early on Wednesday unveiled a series of measures in response to the violence, including authorising police to seal off or impose a curfew on parts of Jerusalem.
A statement from the cabinet also outlined authorisation for the demolition of "terrorists' houses".
The US was swift to condemn the attacks and call for calm.
"I continue to urge all sides to take affirmative steps to restore calm and I will stay in very close touch with leaders in the region in the days ahead," said US Secretary of State John Kerry.
Tuesday's assault on an east Jerusalem bus saw one Palestinian with a pistol and another wielding knives attack some 15 people, police said.
Two Israelis, including a 60-year-old, were killed, and around 10 were wounded, medics and police said.
One attacker was shot dead and the other was wounded.
"I was in my house and I heard between 20 and 30 shots between the police and the terrorists," a local resident said.
At around the same time, in an ultra-Orthodox Jewish area of the city, a Palestinian rammed a car into people at a bus stop and jumped out with a knife.
At least one person was killed and eight wounded, medics said. The attacker was shot and later died, police said.
All three assailants were from the east Jerusalem neighbourhood of Jabel Mukaber, police said, but it was unclear if the attacks were coordinated.
A spokesman for Hamas, the Islamist movement that controls the Gaza Strip, called the attacks "heroic" and said the "intifada is intensifying".
The Jerusalem attacks came after a Palestinian stabbed and wounded a passer-by north of Tel Aviv before being overpowered by civilians.
Police said that attacker was a 22-year-old Palestinian from east Jerusalem and that he was hospitalised after residents severely beat him.
The violence began on October 1, when a suspected Hamas cell shot dead a Jewish settler couple in the West Bank in front of their children.