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Three Israelis have been killed and more than 20 injured in shooting and stabbing attacks in Jerusalem and central Israel, Israeli police say.

Two were killed when two assailants, who were identified as Palestinian, shot and stabbed passengers on a bus in Jerusalem before being shot by police.

Another Israeli died after being run down and stabbed elsewhere in the city.

Later, a Palestinian was killed in clashes with Israeli forces in the West Bank city of Bethlehem, medics said.

Near-daily stabbings by Palestinians have left dozens of Israelis dead and wounded over the past fortnight. Several attackers and at least 17 other Palestinians have also been killed.

Israel's Prime Minister Benjamin Netanyahu said it planned new security measures that would "settle its accounts with the murderers, with those who try murder and with all those who assist them".

"We will employ all means in order to bring quiet back to the citizens of Israel," he told parliament, after convening an emergency session of his security cabinet.

Mr Netanyahu also told Palestinian Authority President Mahmoud Abbas to "stop lying, and stop inciting". Mr Abbas has blamed "acts of aggression" by the Israeli authorities and Jewish settlers for the upsurge in violence.

The militant Palestinian Islamist movement Hamas earlier praised the "heroic operations in Jerusalem and greets the heroes who carried them out".

Escalating tensions

In the bus attack, the two assailants shot several passengers and stabbed others on board the vehicle in East Talpiot, a district in East Jerusalem also known as Armon Hanatziv, police said.

One of the assailants reportedly locked the bus doors in an attempt to stop police from boarding it and passengers from escaping, but police opened fire from outside and shot him.

Minutes later, a man ran over three people with his car at a bus station in the Geula district of West Jerusalem. He then got out of the car and attacked them with a meat cleaver. The attacker was shot by a security guard and seriously wounded.

At the scene: Orla Guerin, BBC News, East Jerusalem

The body of one attacker was still on the bus, his feet visible in the doorway. We saw police carry away a handgun.

One Israeli woman was looking on in tears. "You can't be safe anywhere," she said, "we are worried all the time. Our children are trembling."

Other Israeli residents hurled insults in the direction of Arab residents of the neighbourhood of Jabal Mukaber, just across the road. "They are cannibals," one man shouted. And there were shouts of "death to the Arabs” and “closes their villages".

Locals turned their anger towards Jerusalem's Mayor, Nir Barkat, who visited the scene. "Where is the security?" they asked.

As police responded to this attack, another was unfolding in downtown Jerusalem, where three Israelis were stabbed at a bus stop.

There is a real sense here of not knowing where and when the next attack will come.

Police spokesman Micky Rosenfeld identified all three attackers as residents of the Jabal Mukaber district of East Jerusalem.

Earlier in the morning, a Palestinian stabbed an Israeli man, moderately wounding him, at a bus stop in Raanana, a town north of Tel Aviv, police said. The attacker was captured and reportedly beaten and seriously injured by passers-by.

Not long afterwards, at least four other people were wounded in another knife attack in Raanana, police said. The assailant fled, but was then arrested by police.

Police identified both of the attackers in Raanana as residents of East Jerusalem.

On Tuesday afternoon, clashes between Palestinian protesters and Israeli forces continued in the West Bank after activists called for a "day of rage"

Palestinian medics told the AFP news agency that at least one Palestinian was killed and 15 others wounded by Israeli fire.

In the US, Secretary of State John Kerry said: "The United States condemns in the strongest terms possible the terrorist attacks against Israeli civilians. No matter whom it is, this violence, and any incitement to violence has got to stop."

What is happening between Israelis and Palestinians?

There has been a spate of stabbings of Israelis by Palestinians since early October, and one apparent revenge stabbing by an Israeli. The attacks, in which some Israelis have died, have struck in Jerusalem and elsewhere, and in the occupied West Bank. Israel has tightened security and clashed with rioting Palestinians, leading to deaths on the Palestinian side. The violence has also spread to the border with Gaza.

What's behind the latest unrest?

After a period of relative quiet, violence between the two communities has spiralled since clashes erupted at a flashpoint Jerusalem holy site in mid-September. It was fuelled by rumours among Palestinians that Israel was attempting to alter a long-standing religious arrangement governing the site. Israel repeatedly dismissed the rumours as incitement. Soon afterwards, two Israelis were shot dead by Palestinians in the West Bank and the stabbing attacks began. Both Israel and the Palestinian authorities have accused one another of doing nothing to protect each other's communities.

Is this a new Palestinian intifada, or uprising?

There have been two organised uprisings by Palestinians against Israeli occupation, in the 1980s and early 2000s. With peace talks moribund, some observers have questioned whether we are now seeing a third. The stabbing attacks seem to be opportunistic and although they have been praised by militant groups, Palestinian leader Mahmoud Abbas has said Palestinians are not interested in a further escalation.