Video report by Geraint Vincent: Middle East Correspondent
Six Palestinians were shot dead by Israeli soldiers in Gaza and a Jewish man stabbed four Arabs in southern Israel as tensions mounted in the conflict-ridden region.
An Israeli army official confirmed troops had opened fire on Palestinian protesters, saying its soldiers had shot across into Gaza after stones were thrown at them and burning tyres were rolled too close the border.
Fifty people were wounded in the clashes, medics said.
Earlier in the day, a Jewish man stabbed four Arab men in Dimona, southern Israel, in an attack that was denounced by the Israeli government - including one minister who called it "terrorism".
The most recent clashes came amid rapidly rising tensions, with four Israelis and at least eight Palestinians killed in the last eight days.
Among them was a 13-year-old Palestinian boy, who was shot dead by Israeli forces, as well as an Israeli couple who were killed as the drove between settlements in the West Bank.
Palestinians have been angered by fears Israel wants to change current rules surrounding the al-Aqsa mosque compound in Jerusalem's Old City.
At present, non-Muslim prayer is banned at the holy site, but Jews are allowed to visit.
Israeli President Benjamin Netanyahu has denied he wants to change those conditions, but this has not quelled the alarm of many Muslims in the region.
While the unrest is not on the scale of two previous uprisings in the late 1980s and early 2000s, the increased attacks have prompted concerns of a third "intifada" - a word which literally means "shake" and was applied to both periods of violence.
Netanyahu and Palestinian leader Mahmoud Abbas have both called for calm, while Palestinian police and Israeli security forces continue to work together in an effort to restore order.
Ismail Haniyeh, leader of Palestinian militant group Hamas, praised those who had carried out attacks as "heroes" and said: "This is Friday, this is the day of rage... It is a day that will represent the start of a new intifada in all of the land of Palestine."
The US described violence on both sides as "terrorism", adding that the United States "condemns in the strongest possible terms violence against both Israeli and Palestinian citizens".