However, the family of 19-year-old Kassem Mughrabi said that the incident was an accident.
Mahmoud Mughrabi, Kassem's father, said his son did not have a driving licence and apparently lost control of the car.
"What happened yesterday was a natural road accident. Israel has more 7,000 road accidents a year, not one or two," he said.
"This is a road accident like any other one. The difference here is that they killed my son in cold blood, the car stopped after hitting a wall. It wasn't moving, why kill him?"
Mughrabi said that he wished the soldiers, two of whom were reported to be in a serious condition, a speedy recovery.
Kassem Mughrabi's sister Rasha said he had told her he was going out with friends and would soon return home.
The injured Israeli soldiers were on a tour of Jerusalem ahead of the Jewish New Year holiday next week and were waiting at the intersection near the Arab section of Jerusalem when they were hit.
Shmuel Ben-Ruby, a police spokesman, said they were still treating the incident as an intentional attack and information suggested that disappointment over a failed romance might have been the motive.
He said investigators had found that Mughrabi, who had no prior police record, "wanted to marry his cousin but when she refused he apparently decided to carry out the attack".
|The car was crashed into a group of soldiers waiting to cross the road [AFP]
Ben-Ruby said that the car struck a traffic island and then careened onto a sidewalk, driving for several metres before striking the soldiers and then a wall.
Jacky Rowland, Al Jazeera's correspondent in Jerusalem, said: "The incident took place in West Jerusalem, near Jaffa street, not so far from the Old City, and close to the scene of recent attacks involving tractors."
"There have now been four attacks by Palestinians, not crossing the border, but East Jerusalem residents, who carry Israeli IDs," she said.
In July, two Palestinians who lived in Jerusalem carried out two separate attacks using heavy construction machinery, killing three people and wounding several others. The attackers were shot and killed by police and soldiers.
In March, eight students at a Jewish religious college were shot dead by a Palestinian East Jerusalem resident.
Ehud Barak, Israel's defence minister, called for the home of the attacker to be "destroyed as soon as possible" in order to dissuade others from carrying out similar acts.
The practice of destroying Palestinian attackers homes was halted several years ago after an Israeli supreme court justice ruled it did not deter attackers.