Israeli security forces stand over the body of a man who was killed after allegedly firing on officers in Jerusalem's Old City, February 6, 2020. AHMAD GHARABLI/GETTY

Jerusalem — A spike in Israeli-Palestinian violence on Thursday saw at least three Palestinians killed and a dozen Israeli troops wounded in a rash of attacks and clashes a week after the Trump unveiled his long-awaited Mideast peace plan.

The new spate of attacks put the plan — which was already considered a long-shot because it greatly favors Israel and was rejected outright by the Palestinians — on even shakier ground, and sparked fears of a return to deadly rounds of violence of the past. The plan has sparked calls by Israeli nationalists for Israel to annex parts of the West Bank — land Palestinians want for their hoped-for state — and has set off tensions in the region.

The violence escalated Thursday morning. The first incident was a Palestinian motorist who slammed his car into a group of Israeli soldiers, wounding 12 before fleeing the scene, the Israeli military said. In the West Bank, two Palestinians died after clashes broke out with Israeli troops, according to Palestinian hospital officials.

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And later, Israeli police said they shot and killed a Palestinian who opened fire at forces in Jerusalem's Old City, lightly wounding one officer.

Israeli military spokesman Lt. Col. Jonathan Conricus said one of the 12 injured soldiers in Jerusalem was seriously hurt, while the others sustained minor injuries. Israeli police spokesman Micky Rosenfeld said the incident was being treated as a "terror attack," and said Israeli forces were searching for the assailant.

An Israeli policeman inspects the site of a car-ramming attack that the Israeli military said was carried out by a Palestinian in Jerusalem on February 6, 2020. OREN BEN HAKOON/AFP/Getty

Palestinian hospital officials said a 19-year-old was killed in clashes in the West Bank city of Jenin. Six others were wounded in the confrontation. In a separate incident also in Jenin, a member of the Palestinian security forces who was shot by Israeli troops later died. That violence came just hours after Israeli forces shot and killed a 17-year-old Palestinian during clashes with demonstrators elsewhere in the West Bank on Wednesday.

"Attacks from Gaza, an attack in Jerusalem, signs of a rise in hostile activity in Jenin. Yesterday friction in Hebron. We are not trying to escalate the situation while understanding the complexity and sensitivity of the situation," Conricus said, stopping short of directly linking the spate of violence to the unveiling of Mr. Trump's plan.

In the first Jerusalem incident, the troops were out on a late-night "educational heritage tour," walking near a popular entertainment district in Jerusalem when the motorist rammed his car into them and fled.

While it did not claim responsibility for the attack, the Islamic Jihad militant group praised the car ramming as "the beginning of a new confrontation over Trump's plan."

Israeli Prime Minister Benjamin Netanyahu vowed to have the assailant apprehended. "It's just a matter of time — and not much time," he said in a statement.

Such acts of violence were common in Jerusalem during a low-level wave of near-daily attacks over the last decade, but they tapered off and car rammings have become infrequent in recent years.

Conricus said troops were carrying out the demolition of a home in the West Bank belonging to a militant allegedly involved in a deadly attack. He said there was a "sizable riot" at the scene by Palestinians who threw Molotov cocktails at troops, who then came under sniper fire. Conricus said forces responded to the violence with their own sniper fire, saying a Palestinian shooter was killed.

Palestinian men carry the body of 19-year-old Yazan Abu Tabikh, who was killed during a raid by Israeli forces in Jenin, during his funeral in the northern West Bank city on February 6, 2020. JAAFAR ASHTIYEH/Getty

Jenin governor Akram Rajoub said the 19-year-old casualty was a student at an academy that trains budding police officers, and was throwing stones at the troops.

Also Thursday, Israel struck Hamas positions in the Gaza Strip after three mortar shells were fired at Israel. There was no immediate report of injuries on either side.

Unveiled last week at the White House with much fanfare, Mr. Trump's plan envisions a disjointed Palestinian state that turns over key parts of the West Bank to Israel. It sides with Israel on key contentious issues that have bedeviled past peace efforts, including borders and the status of Jerusalem and Jewish West Bank settlements, and attaches nearly impossible conditions for granting the Palestinians their hoped-for state.

The plan was greeted ecstatically in Israel, with Netanyahu vowing to speed ahead with annexing parts of the West Bank. But under pressure from the U.S. administration he appears to be scaling back on that promise.

The Palestinians dismissed the plan as "nonsense" and have promised to resist it.

The Palestinians, as well as much of the international community, view the settlements in the West Bank and annexed east Jerusalem - territories seized by Israel in the 1967 war - as illegal and a major obstacle to peace.