Israel’s military says it is on the hunt for the Palestinian “terrorist” who rammed his car into a dozen soldiers in Jerusalem on Thursday, triggering a new spike of violence in the region.

The fresh Israeli-Palestinian clashes have left at least three Palestinians dead and come just days after President Trump and Israeli Prime Minister Benjamin Netanyahu revealed a Middle East peace plan meant to bring an end to the decades-long conflict.

“Early this morning, a Palestinian rammed his car into a group of IDF soldiers in Jerusalem,” the Israel Defense Forces said. “The terror attack injured 12 soldiers, one of whom is in serious condition.

“We are currently pursuing the terrorist,” it added.

Israeli police officers inspect the scene of a ramming attack in Jerusalem on Thursday. (AP)

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In the West Bank city of Jenin on Thursday, two Palestinians – including a 19-year-old – died after clashes broke out with Israeli troops, according to Palestinian hospital officials.

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

“Attacks from Gaza, an attack in Jerusalem, signs of a rise in hostile activity in Jenin… we are not trying to escalate the situation while understanding the complexity and sensitivity of the situation,” Israeli military spokesman Lt. Col. Jonathan Conricus said.

In the Jerusalem car-ramming incident, the troops were out on a late-night “educational heritage tour,” walking near a popular entertainment district in Jerusalem when the driver plowed his car into them and fled.

Palestinians inspect a house after it was demolished by the Israeli army in the West Bank city of Jenin on Thursday. (AP)

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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,” The Associated Press reports.

Netanyahu vowed to have the assailant apprehended. “It’s just a matter of time — and not much time,” he said in a statement.

In the Jenin flare-up involving the 19-year-old, Conricus said troops were carrying out the demolition of a home 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.

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

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In a separate incident also in Jenin, a member of the Palestinian security forces who was shot by Israeli troops later died.

Also on 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.

Fox News’ Andrew O’Reilly and The Associated Press contributed to this report.