JERUSALEM (AFP) - Israeli police announced on Sunday (Oct 4) that Palestinians will be banned from accessing Jerusalem's Old City for two days after twin attacks on Israelis that also left the perpetrators dead.

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

The move will affect the vast majority of Palestinians in annexed east Jerusalem who do not live inside the Old City, meaning that only Israelis, tourists, residents of the area, business owners and schoolchildren will be able to enter, they said.

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

The usually bustling alleyways of the walled Old City were mostly quiet on Sunday morning, with stores closed and hundreds of police guarding entrances.

A group of around 50 women as well as several men protested outside a gate before demonstrating inside the neighbourhood, where they were blocked by police.

Police later fired stun grenades and rubber bullets to disperse protesters at the gate, an AFP journalist reported.

The Palestinian government denounced "Israeli escalation" on Sunday, in response to the ban. "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.

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

A Palestinian said to be an Islamist militant killed two Israeli men and injured a woman and a toddler in a knife and gun attack in Jerusalem on Saturday, in a fresh escalation of violence.

A two-year-old child was slightly injured in the leg and taken to hospital as a result of Saturday's attack, and a woman was in serious condition, rescue services said. Police spokesman Micky Rosenfeld said it appeared the child had been shot.

The attacker reportedly took a gun from one of the male victims and fired at police when they responded after being alerted, before he was himself shot dead.

Police named him as Mohannad Shafiq Halani, aged 19, from a village near Ramallah in the West Bank.

Militant group Islamic Jihad said he was one of its members, but did not claim responsibility for the attack.

Media reports said three of the victims were members of the same ultra-Orthodox family on their way to pray at the Western Wall.

In the second incident on Saturday, a Palestinian man stabbed a passer-by in west Jerusalem before being shot dead by police while he was fleeing the scene. The victim was injured, police said.

The attack in the Old City came with Israeli security forces on alert after recent clashes at the city's flashpoint Al-Aqsa mosque compound and the murder in the West Bank of a Jewish settler couple in front of their young children.

Israeli President Reuven Rivlin said his country was fighting "a battle against terrorism" and vowed to go after "the killers of innocent people".

Opposition leader Isaac Herzog accused Prime Minister Benjamin Netanyahu of "losing control of Israel's security".

The United States condemned the attack, with State Department spokesman John Kirby saying Washington was "very concerned about mounting tensions in the West Bank and Jerusalem".

Palestinian militant group Hamas meanwhile praised the attack as "a heroic act of resistance".