Both Palestinians were from east Jerusalem, which was captured by Israel in 1967 along with the West Bank. The 208,000 Palestinians who live there are not Israeli citizens but carry Israeli ID cards that allow them freedom of movement throughout Israel, unlike West Bank Palestinians.
Police said in the latest attack, a civilian driving nearby saw what was happening, jumped out of the car and shot the driver. A border policeman who rushed to the scene also shot the driver.
Police sealed off possible escape routes into predominantly Arab east Jerusalem and were searching for two suspects who fled, police spokesman Micky Rosenfeld said.
Palestinian President Mahmoud Abbas condemned the attack. And Obama, speaking from Jordan hours before he is to arrive in Israel, deplored it as "a reminder of what Israelis have courageously lived with on a daily basis for far too long."
"I will always support Israel in confronting terrorism and pursuing everlasting peace and security," Obama said.
Police identified the perpetrator of Tuesday's attack as 22-year-old Ghassan Abu Teir, an east Jerusalem resident related to a militantly anti-Israel politician from the Islamic Hamas party, Mohammed Abu Teir.
The attacker struck a busy part of downtown Jerusalem, several hundred yards from the luxury King David hotel where Obama is scheduled to stay. The incident took place about seven hours before Obama was to arrive in Israel.
"I was driving on the main road when the (vehicle) hit me in the rear on the right hand side," said the bus driver, Avi Levi.
"After I passed him, he turned around, made a U-turn and rammed the windows twice with the shovel. The third time he aimed for my head, he came up to my window and I swerved to the right, otherwise I would have gone to meet my maker."
Like the perpetrator of the previous attack, the driver in Tuesday's incident was a Palestinian from east Jerusalem with an Israeli residence permit and he drove the same type of front loader, police said. Israeli police called it a "terror attack" but no group immediately claimed responsibility.
Witness Moshe Shimshi said the Palestinian driver, who was wearing a large, white skullcap commonly worn by religious Muslims, slammed into the side of the bus, then sped away and went for a car.
"He didn't yell anything, he just kept ramming into cars," Shimshi said.
Shimshi said he saw a man run toward the construction vehicle firing a pistol.
"After a few shots, I saw the driver shake and fall, and then he didn't move any more."
After the Jerusalem police chief Ilan Franco said a border police officer arrived and shot at the driver "to make sure he was killed." In the attack earlier this month, the driver of the construction vehicle was shot and presumed dead - only to revive and carry on with his attack before being shot dead.
Jerusalem Mayor Uri Lupolianski was in the area when he heard a commotion and rushed over.
The attacker "is from east Jerusalem," he said. "They keep on inventing ways to attack us," he said. "Every work tool has become a weapon."
The three latest attacks in Jerusalem have been carried out by Palestinians from the eastern sector of the city's eastern sector, where they make up less than a third of the city's population. Many east Jerusalem Palestinians work in construction in the Jewish parts of the city.
Relatives said Abu Teir did not belong to a radical faction, and had worked on construction vehicles for the past seven years.
