The shooting took place near the Jewish settlement of Ofra, where another gunman wounded seven people in a separate attack on Sunday.
A Palestinian gunman got out of a auto and opened fire at a bus stop outside a West Bank settlement on Thursday, killing two Israeli soldiers before speeding away, the Israeli military said. An army spokesperson was unable to confirm reports that the assailant had targeted Israeli soldiers.
Barghouti has been the subject of a massive man hunt throughout the West Bank after he was involved in a drive-by shooting that left seven people critically wounded and one newborn baby dead.
On Wednesday, Israeli forces killed Salah Barghouti, a Palestinian suspect wanted in the drive-by shooting earlier this week at a West Bank bus stop.
Doctors tried to save her baby boy with an emergency caesarean but he died on Wednesday and was laid to rest in Jerusalem.
A seriously injured man and woman were both taken to hospitals in Jerusalem for treatment.
A second attacker was allegedly wounded in the firefight between Israeli Yamam forces and Palestinian Authority terrorists, according to a report broadcast Wednesday by Israel's Channel 2 television news.
Israeli police said Ashraf Naalweh was found armed near the West Bank city of Nablus and was killed during an arrest raid.
The killings extend a violent week that began with a shooting outside a West Bank settlement on Sunday.
Israeli media reported that a passing vehicle opened fire outside the settlement, but it was not clear if the gunmen had fled the scene or were stopped.
The two were employees of the recycling company where Naalwa worked.
In another incident, a Palestinian stabbed two Israeli border police in Jerusalem's Old City before being shot dead, in the bloodiest 24 hours to hit the West Bank and Jerusalem in months.
In recent days Hebrew posters have been erected in the West Bank encouraging the killing of Abbas.
Israel captured the West Bank, the Gaza Strip and east Jerusalem in the 1967 Mideast war.
Palestinian Hamas hailed Sunday's shooting, saying it proved "resistance" was still alive in the West Bank. All settlements are deemed illegal under global law.
The attacker, a 26-year-old Palestinian from the West Bank, was shot dead by the officers. Israel has said it will look into the incident.
Netanyahu has been under vast pressure to confront Hamas since late March, when his crackdown on the Palestinian protests at the Gaza border, dubbed the Great March for Return, backfired and prompted retaliatory attacks from the resistance movement.