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Three Palestinians were killed in a shootout with Israeli security forces in Jerusalem's Old City early on Friday, Israeli police claimed.

They arrived at the sacred hilltop compound, known to Muslims as the Haram al-Sharif and to Jews as Temple Mount, and walked toward one of the Old City gates nearby, according to police spokesperson Luba Simri.

"When they saw policemen they shot toward them and then escaped toward one of the mosques in the Temple Mount compound," she said.

"A chase ensued and the three terrorists were killed by police."

A number of people were wounded in the attack, including two Israeli police officers who were taken to hospital after being critically injured.

The three Palestinians were shot and left on the ground bleeding while medics were reportedly prevented from approaching them, witnesses told .

Amateur video broadcast on Israeli TV stations showed a few seconds of what appeared to be confrontation between Israeli security forces and the Palestinians.

In the video, several people - only visible as dark figures in the footage shot from a distance - were running inside the compound. At one point, one of the figures dropped to the ground. In another moment, a puff of smoke, possibly from gunfire, was visible.

Police locked down the area and the al-Aqsa mosque compound at the holy site was closed for Friday prayers - the highlight of the Muslim religious week.

The compound is the holiest site in Judaism and the third-holiest in Islam, after Mecca and Medina in Saudi Arabia.

The site has been a flashpoint for violence in the past, with friction there sparking major rounds of Israeli-Palestinian violence, including a Palestinian uprising against Israeli occupation that lasted several years.

A wave of unrest that broke out in October 2015 has claimed the lives of at least 277 Palestinians, 42 Israelis, two Americans, two Jordanians, an Eritrean, a Sudanese and a Briton.

Israeli authorities say most of the Palestinians killed were carrying out knife, gun or car-ramming attacks.

Others were shot dead in protests and clashes, while some were killed in Israeli air strikes on the Gaza Strip.

The violence has greatly subsided in recent months.