A Palestinian teenager was shot dead in the West Bank and an Israeli air strike killed a pregnant woman and toddler in Gaza, as unrest threatened to spiral into a full-scale intifada.
Four Israelis were also wounded near a kibbutz, after more than 10 days of clashes between Israeli forces and Palestinians in the occupied West Bank and annexed east Jerusalem, as well as a series of Palestinian stabbings of Jews.
Hamas has already branded the spiralling violence between Israelis and Palestinians an intifada and called for further unrest.
The airstrike, launched in retaliation over two rockets fired at Israel, demolished a house in northern Gaza, killing Nur Hassan, 30, and her two-year-old daughter Rahaf.
A spokesman for Hamas, which controls the coastal enclave, said "this shows the occupation's desire to escalate".
"We warn the occupation against continuing this foolishness," said Sami Abu Zuhri.
Israel had said it was targeting Hamas' arms manufacturing facilities.
Israeli forces shot dead the Palestinian teenager, identified by the Palestinian health ministry as Ahmad Sharake, 13, during clashes near the West Bank city of Ramallah.
Medics said dozens of Palestinians were also shot and wounded in other clashes across the West Bank.
Sharake, from Jalazun refugee camp, was killed in clashes that broke out as hundreds of Palestinians near Ramallah attempted to approach a road to throw stones and firebombs at settlers' cars.
Within hours of the teenager's death, four Jews were attacked near Gan Shmuel kibbutz in northern Israel by an Arab Israeli who rammed them with his car and then lunged at them.
Israel's Shin Bet internal security agency identified the perpetrator as 20-year-old Alla Zayud from the northern town of Umm el-Fahm.
The Israeli army revealed that two soldiers were hit by the car, with one of them seriously injured, and two civilians were stabbed.
The attack near the kibbutz was the 15th stabbing of Israelis since October 3, but the first by an Arab Israeli to cause injury -- rather than by Palestinians from east Jerusalem or the West Bank.
In a revenge stabbing, a 17-year-old Jew in the southern Israeli city of Dimona wounded two Palestinians and two Arab Israelis on Friday.
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European Union foreign policy chief Federica Mogherini appealed against the escalation of violence on Sunday in separate phone calls to Israeli Prime Minister Benjamin Netanyahu and Palestinian Authority President Mahmud Abbas.
"(I) talked now with Prime Minister Netanyahu and President Abbas on escalation of violence. Need to stop acts of terror and to avoid disproportionate reactions," Mogherini said in a tweet.
Rioting has seen Palestinians throwing stones and firebombs at Israeli forces throughout the area, who have responded with live fire, rubber bullets, tear gas and stun grenades.
- Mounting frustration -
Palestinian frustration has mounted with efforts towards statehood at a standstill and Israel's occupation continuing, and a recent poll showed that a majority of favour a return to armed uprising in the absence of peace talks.
Netanyahu has ordered the emergency call-up of 16 reserve border police units to reinforce officers in east Jerusalem and throughout Israel.
But while Netanyahu and Abbas have sought to avoid an escalation, frustrated Palestinian youths have defied efforts to restore calm.
On Sunday, the cabinet approved a four-year minimum prison term for people convicted of throwing stones at moving cars.
An Israeli security official, in a cabinet briefing on Sunday, charged that senior members of the Palestinian Authority and Abbas's Fatah party were inciting violence.
Meanwhile Arab Israelis held demonstrations throughout northern Israel on Sunday, blocking roads and burning tyres. Police said the protests were "contained" and did not report any arrests.
Earlier Sunday, an explosion seriously wounded a Palestinian woman and lightly injured an Israeli policeman at a West Bank checkpoint near Maale Adumim settlement.
After a policeman told 31-year-old Israa Jaabis to stop, she shouted "Allahu Akbar" (God is greatest) and blew up a gas cylinder in her car, security forces said.