Earlier, five Palestinians were killed on Sunday after an Israeli raid in the occupied West Bank sparked gunbattles with Hamas members, two of them in Burqin
Three Palestinians were killed Thursday by Israeli fire, including a woman who tried to stab officers in Jerusalem, an insurgent shot during West Bank clashes and a Gazan who approached the border fence.
The violence comes days after an Israeli raid on so-called insurgents in the occupied West Bank left five Palestinians dead.
At dawn in Jerusalem, the sound of gunshots rang through the Old City, with the body of a woman lying on a stone street that leads to the Al-Aqsa mosque, an AFP journalist said. She was later draped in a survival blanket.
Police said she had attempted to stab officers after being stopped for a check because her conduct aroused suspicion.
"During the questioning, the terrorist pulled out a knife and tried to stab the officers. They immediately responded with gunfire and neutralised her," a statement said, noting medics later pronounced her dead.
The woman was identified by Palestinian officials as Israa Khozaimieh, 30, from Qabatiya in the northern West Bank.
The attempted attack did not result in any Israeli casualties.
Israeli security forces are stationed at each entrance to the Al-Aqsa mosque compound, Islam's third holiest site, known to Jews as the Temple Mount, the holiest site in Judaism.
The compound lies in east Jerusalem, which Israel occupied in 1967 and later annexed in a move never recognised by the international community.
West Bank clash
In a separate incident in Burqin, in the northern West Bank near Jenin, Israeli troops and border police conducted an overnight operation "to arrest suspects and locate weapons," a police statement said.
"During the operation, an armed terrorist fired at the forces who were operating in the village during a riot," police said.
"Border police forces responded with gunfire toward the terrorist and neutralised him," police said, with a spokesman confirming his death to AFP.
Palestinian isurgency group Islamic Jihad said the man killed was Alaa Zayoud, 22, a member of its military wing.
No Israeli forces were wounded in the incident in the West Bank, a Palestinian territory under Israeli military occupation since 1967.
On Sunday, five Palestinians were killed after an Israeli raid in the West Bank sparked gun battles with Hamas members, two of them in Burqin, officials said. One of those killed in Burqin on Sunday was an Islamic Jihad member, and the movement said on Thursday that Zayoud had "joined" him.
Hamas, the insurgent rulers of the Gaza Strip, issued a statement in support of the "martyrdom" of Zayoud, saying "armed resistance and comprehensive confrontation" with Israel were the way to expel "settlers" from "our occupied land".
In a third and unrelated incident in Gaza, Israeli troops "spotted three suspects approaching the security fence," an army statement said.
"One of the suspects was seen carrying a suspicious backpack and digging in the ground. (Israeli) troops at the scene fired towards the suspect," the army said, adding that it was reviewing the incident and was "aware of reports that a Palestinian was killed."
Gaza's Health Ministry said the man was killed and identified him as Mohammad Abu Ammar, 40.