Israel police have now banned Palestinians from East Jerusalem from entering the Old City for two days.
On Saturday night, a palestinian killed 2 Israeli men and wounded a woman and a toddler in a knife and gun attack in the Old City. Police shot dead the palestinian attacker.
In a separate incident early on Sunday, a Palestinian stabbed and wounded a passer-by in West Jerusalem before being shot dead by police while fleeing.
The attacks came with Israeli security forces already on alert after recent clashes at the Al-Aqsa Mosque compound and the surrounding Old City, as well as the murder in the occupied West Bank of a Jewish settler couple in front of their young children.
The restrictions on the Old City in occupied East Jerusalem only allow access to Israelis, tourists, residents of the area, business owners and students, police said.