Israel took the rare and drastic step of barring Palestinians from Jerusalem's Old City on Sunday as tensions mounted after attacks that killed two Israelis and wounded a child.

The restrictions will be in place for two days, with only Israelis, tourists, residents of the area, business owners and students allowed, police said.

Worship at the sensitive Al-Aqsa mosque compound will be limited to men aged 50 and over. There will be no age restrictions on women, and worshippers will be allowed to enter through one specific gate.

The Palestinian government denounced "Israeli escalation" after the announcement of the ban, which Israeli Public Security Minister Gilad Erdan called unprecedented.

The usually bustling alleyways of the walled Old City were mostly quiet on Sunday morning, with stores closed and hundreds of police guarding entrances. Some shops began gradually opening later in the day.

About 300,000 Palestinians live in Israeli-annexed east Jerusalem, where the Old City is located.

The attacks late on Saturday and early on Sunday came with Israeli security forces already on alert after recent clashes at the Al-Aqsa 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.

On Saturday night, a Palestinian said to be an Islamist 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 on Sunday, a 19-year-old Palestinian stabbed and wounded a passerby in west Jerusalem before being shot dead by police while fleeing.

There were clashes elsewhere overnight and on Sunday, and the Red Crescent reported 77 Palestinians had been wounded from both live rounds and rubber bullets.

Another 139 had been treated for tear gas inhalation and six for injuries sustained in beatings by soldiers or Jewish settlers, a Red Crescent spokeswoman said.

Clashes broke out in areas including Jenin in the West Bank, where Israeli soldiers raided a refugee camp to arrest a Hamas official, and the east Jerusalem neighbourhood of Issawiya, where the attacker in Sunday morning's stabbing, identified as Fadi Alloun, was from.