On Wednesday morning police blocked entrances to Jabal Mukaber, a district that is home to three men accused of killing three Israelis on Tuesday.
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.
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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.
Speaking for the first time since the upsurge in violence began, Palestinian Authority President Mahmoud Abbas said Israeli actions were “threatening to spark a religious conflict that would burn everything”.
He also accused Israel of carrying out “executions of our children in cold blood”, highlighting the case of a 13-year-old Palestinian boy who was shot by Israeli police after he and a 15-year-old stabbed an Israeli on Monday.
Israeli Prime Minister Benjamin Netanyahu has described the Palestinian leader’s comments as “lies and incitement”, adding that the boy was alive in hospital, the Jerusalem Post reports.
He said on Tuesday the new security measures were aimed at “those who try murder and with all those who assist them”.
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