Israeli border police shot dead a Palestinian at a checkpoint near Jerusalem, Israeli police and family members said Friday, in the second fatal shooting by Israeli forces in 12 hours.

Police spokesman Micky Rosenfeld said the incident occurred around midnight (2200 GMT), when a man ran at a border police officer with a knife, prompting him to open fire.

"A Palestinian who arrived at the area ran out of a vehicle toward border police who were there on patrol," Rosenfeld said.

"The Palestinian had a knife in his hand and a border police officer responded by firing shots at the suspect who was injured seriously and pronounced dead a short while after."

Family members named him as Anas al-Atrash, 23, from the southern West Bank city of Hebron and said the shooting happened at the Wadi Nara checkpoint between Abu Dis and Bethlehem.

"They stopped my two sons at the checkpoint and they were waiting to be checked. Then the soldiers came to the car and opened the door and my son tried to get out and they shot him," his father, Fuad al-Atrash told AFP, referring to the border police.

The brother was arrested, he added.

On Thursday night, Israeli forces shot dead another Palestinian near the northern West Bank city of Nablus, saying he had fired a flare gun at Israelis at Tapuah Junction.

The body of the man, identified as Bashar Habaneen, 29, was handed over to Palestinians by the Israeli army on Friday morning, Palestinian security sources said.

Habaneen, from the village of Mirka near the northern West Bank city of Jenin, was a lecturer at Tulkarem university who was not known to have belonged to any political or militant faction.

Later on Friday morning, two Israelis were lightly wounded by a molotov cocktail thrown at their car near the Tekoa settlement, the Israeli army said.

The uptick in violence came as US-brokered peace talks, which resumed in late July, were faltering, and US Secretary of State John Kerry was in the region in an attempt to put them back on track.

In an interview with Israeli and Palestinian television on Thursday, Kerry warned that a failure to make peace could trigger new Palestinian violence.

"The alternative to getting back to the talks is the potential of chaos," he said.

"I mean, does Israel want a third intifada?" the top US diplomat asked, using the Arabic word for uprising.