On Wednesday morning police blocked entrances to Jabal Mukaber, a district that was home to three men accused of killing three Israelis on Tuesday.
Later, police said they shot dead a Palestinian who had stabbed an Israeli woman at Jerusalem's main bus station.
Another Palestinian tried to stab a policeman near the walled Old City.
He, too, 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. (s:bbc)