Israeli forces have shot dead a 16-year-old Palestinian girl after she allegedly attempted to stab a border policeman at a checkpoint between the occupied West Bank and Jerusalem, according to local media and police reports.

Israeli border police opened fire on Samah Zuheir Mubarak, a student from the West Bank city of Ramallah, at the al-Zaeem checkpoint, which separates an illegal Jewish settlement in the West Bank from a neighbourhood that lies in occupied East Jerusalem.

Mubarak's family, based in the Gaza Strip, told local media that Israeli forces killed their daughter in "cold blood".

In a video released by Israeli police, Mubarak is seen walking towards the checkpoint. In another clip, she is seen standing near a vehicle and a group of Israeli forces. After what appears to be a brief exchange, the police officer backs away, Mubarak is shot by Israeli forces at close range and falls to the ground.

Another clip shows Israeli forces searching through her belongings including books and school supplies as they emptied her bag.

Yoram Halevi, Israel's Jerusalem police chief, said the Palestinian girl pulled out a knife and tried to "stab" Israeli soldiers at the al-Zaeem checkpoint, and was shot.

"It's not clear what the background is, what is the reason [behind her arrival to the checkpoint]," he said, adding the incident is being "investigated".

The incident comes days after at least three other Palestinians were killed by Israeli forces and settlers.

On Saturday, 38-year-old Hamdi Naasan succumbed to his wounds in the West Bank village of al-Mugheir after Israelis from a nearby settlement fired shots.

Ayman Hamed, 18, was laid to rest in his village of Silwad after the Israeli army shot and killed him on Friday for allegedly throwing stones.

Israeli police also killed Riyad Shamasneh during a high-speed chase near the Old City's Damascus Gate in East Jerusalem on Saturday morning.

A number of local and international human rights groups have raised concerns that Israeli security forces have used excessive force when confronting Palestinians who carried out attacks or were suspected of doing so.

The Israeli police relaxed its open-fire regulations in December 2015, permitting officers to open fire with live ammunition on those throwing stones or firebombs as an initial option, without having to use non-lethal weapons first.