Israeli forces have begun a major security operation in Arab areas of occupied East Jerusalem, after a surge in attacks by Palestinians.
Police blocked on Wednesday morning entrances to Jabal Mukaber, a district where three men accused of killing three Israelis on Tuesday came from.
The Israeli military also deployed hundreds of soldiers to assist.
Later, police said they shot dead a Palestinian who stabbed an Israeli woman at Jerusalem's main bus station.
A Palestinian also attempted to stab a policeman at the Damascus Gate of the walled Old City, but was shot dead by police, they added.
Since the beginning of October, seven Israelis have been killed and dozens wounded in shooting and stabbing attacks, the Israeli authorities say.
At least 30 Palestinians have also been killed, including assailants, and hundreds have been injured, according to the Palestinian health ministry.
'Recipe for harassment'
On Tuesday night, Israel's security cabinet authorised police to close or surround "centres of friction and incitement" in Jerusalem.
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It also announced that the homes of Palestinians who attacked Israelis would be demolished within days and never rebuilt, and that their families' right to live in Jerusalem would be taken away.
On Wednesday morning, a police spokeswoman told the AFP news agency that checkpoints were being set up at "the exits of Palestinian villages and neighbourhoods in East Jerusalem".
Israeli newspapers later reported that several entrances to Jabal Mukaber had been blocked by police, with neither people nor vehicles allowed in or out. Several more areas were expected to be closed off by the end of the day.
At the scene: Jonny Dymond, BBC News, East Jerusalem
Across some roads leading into Arab neighbourhoods, a police vehicle blocks access; at other points, heavily armed police keep guard; at one access point, what was a lightly-staffed police checkpoint has been beefed up.
For years, Israel has tightly controlled access in and out of the West Bank and Gaza, where the vast majority of Palestinians live. East Jerusalem's checkpoints are not like the ones around the West Bank and Gaza; they are much more informal affairs. But they are, for the first time since 1967, restricting access to and from largely Arab East Jerusalem.
How long they will last is difficult to call. East Jerusalem's residents have the right to move freely through the city and Israel. It doesn't seem feasible to cut off whole neighbourhoods for long. And the roadblocks and checkpoints strike at the idea promulgated by the Israeli right that Jerusalem is the undivided capital of the Israeli state.
The checkpoints have the feel of short-term solution to an acute security problem. But with Israelis mourning their dead, and in fear of their lives, there is extraordinary pressure on the government to act.
Human Rights Watch warned on Tuesday night that locking down parts of East Jerusalem would "infringe upon the freedom of movement of all Palestinian residents rather than being a narrowly tailored response to a specific concern".
"The checkpoints are a recipe for harassment and abuse," said Sari Bashi, the group's Israel/Palestine country director, in a statement.
Meanwhile, the Israeli military said it was preparing to deploy six companies to assist police. Three hundred soldiers are already providing additional security under police command.
The security cabinet's decisions were made after the bloodiest day in Jerusalem since the latest wave of unrest began in early October.
In Tuesday's first attack, two Palestinian men boarded a bus and began shooting and stabbing passengers, killing two Israelis, police said. Police shot dead one of the assailants and wounded the other.
Locations of Tuesday's attacks in Jerusalem
Just a few minutes later, another Palestinian rammed his car into a bus stop before getting out and stabbing people. The attacker was fatally shot by a security guard.
There were also two separate knife attacks in Raanana, a town in central Israel. Police identified the assailants as Palestinian residents of East Jerusalem.
Reuters
Clashes between Palestinian protesters and Israeli soldiers meanwhile continued in the West Bank after Palestinian activists called for a "day of rage".
Palestinian medics said one Palestinian was killed by Israeli fire in Bethlehem.
The BBC's Yolande Knell in Jerusalem says the violence, coming at a time when peace prospects seem dim, has fuelled a sense of panic in Israel and raised fears of a new Palestinian uprising, or intifada.
What is happening between Israelis and Palestinians?
There has been a spate of stabbings of Israelis - several of them fatal - by Palestinians since early October, and one apparent revenge stabbing by an Israeli. The attackers have struck in Jerusalem and central and northern Israel, and in the occupied West Bank. Israel has tightened security and its security forces have 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.
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