The attacker was a member of the Palestinian militant group Hamas, which later praised the attack, calling it revenge for recent Israeli actions at the sacred Al-Aqsa Mosque.
In a two-stage assault, Ibrahim al-Akri, 38, drove a van first into a station in the predominantly Arab East Jerusalem neighborhood of Sheikh Jarrah, striking, among others, Jadan Assad, a 38-year-old Border Patrol captain, authorities said. Akri then drove farther down the street before getting out of the van with a bar, attacking surrounding cars. He was then shot and killed by police.
Assad later died of his injuries, according to authorities, and at least three others are reportedly in critical condition.
A Hamas statement issued Wednesday afternoon praised Akri, an East Jerusalem resident, as a “son of the movement.” The statement said the attack was a natural reaction to recent Israeli settler and security actions at the Al-Aqsa Mosque compound -- known as the Temple Mount to Jews -- the third-holiest site in Islam and the holiest in Judaism.
Muslim worshipers in the compound on Wednesday clashed with Israeli police, accused by those praying there of storming the complex.
The compound -- known as Haram al-Sharif, or the Noble Sanctuary to Muslims -- has been at the center of recent growing tension in Jerusalem.
Clashes and attacks have been growing for months, fueling fears of a third Palestinian "Intifada," or uprising.
"We are in the midst of a struggle for Jerusalem and I have no doubt that we will triumph," the prime minister said, according to the Haaretz newspaper. "We are deploying all the forces that we can. It could be a prolonged struggle and we need to unite the entire nation behind it."
Later in the day, there was another hit and run, this time in the West Bank, some 18 miles south of Jerusalem, Israeli Police Superintendent Micky Rosenfeld confirmed.
“Near the El Arub junction, Arab vehicle struck two people. Both injured moderately. Road blocks set up in area. Incident suspected attack," Rosenfeld tweeted.
“Total of 3 people injured in terrorist attack in Gush Etzion area, El Arub. 1 seriously, 2 moderately. The injured being taken to hospital," Rosenfeld added.
The area is technically in the jurisdiction of the Israel Defense Forces, not the police.
ABC News' Bruno Nota contributed to this report.