Israeli security forces have shot dead two Palestinians youths during clashes close to the border with the Gaza Strip.
Medical officials said the youths, aged 12 and 15, were killed near Khan Younis.
Earlier, there were two stabbing attacks by Palestinians in Jerusalem, with Israeli police shooting the attackers dead, Israeli officials said.
The past week has seen a spate of violence.
An Israeli army spokeswoman said the boy and teenager killed near Khan Younis were in a no-go security zone as protesters were hurling burning tyres and stones at soldiers.
There were also protests along the border fence in the northern Gaza Strip. Israeli officials said five people were arrested after dozens of Palestinians briefly breached the border.
In Jerusalem, two policemen were stabbed near Damascus gate on Saturday afternoon. A teenager stabbed two Israelis nearby earlier in the day.
There were also clashes on Saturday after the funeral of a Palestinian man who had been shot during unrest at the Shuafat refugee camp in East Jerusalem and later died of his injuries.
The heightened tension between Israelis and Palestinians began in mid-September when Palestinian protesters clashed with Israeli police at the al-Aqsa mosque/Temple Mount compound, a site sacred for both Muslims and Jews.
Saturday's stabbings were the latest in a wave of attacks by young Palestinians on Israelis that have fuelled tension in East Jerusalem and the West Bank. Israel has responded with tougher security measures.
The violence has spurred talk from Hamas, which dominates Gaza, of a new Palestinian intifada, or uprising.
But the clashes have not yet reached the scale of previous intifadas, with no clear mass movement or leadership so far emerging.
Police said Saturday's first stabbing had been carried out by a 16-year-old Palestinian. Two ultra-Orthodox Jewish men in their 60s were wounded, police and medics said.
Later, another Palestinian stabbed two police officers just outside the Old City, police spokesman Micky Rosenfeld said. Police opened fire and killed the assailant, but also wounded one of their colleagues, he said.
Friday was the deadliest day since the recent violence erupted.