"The Palestinian government denounces the Israeli escalation policy by Israeli occupation authorities against our people in occupied Jerusalem and the West Bank," it said in a statement after the imposition of the two-day ban.
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On Saturday night, a Palestinian alleged to be a militant killed two Israeli men and wounded a woman and a toddler in a knife and gun attack in the Old City. Police shot dead the attacker.
In a separate incident early Sunday, a Palestinian stabbed and wounded a passerby 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 surrounding Old City, as well as the murder in the West Bank of a Jewish settler couple in front of their young children.
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The restrictions on the Old City only allow access to Israelis, tourists, residents of the area, business owners and students, police said.
Worship at the sensitive Al-Aqsa mosque compound will be restricted to Old City residents and Arab Israelis, and limited to men aged 50 and above. There will be no age restrictions on women. They will be allowed to enter through one specific gate.
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