The incident near the Israeli settlement of Ofra came ahead of the Jewish Passover holiday beginning on Monday, which has raised fears of an upsurge in violence.
The Israeli police believes that the Palestinian driver, identified as Malek Ahmad Hamed, 21, from Silwad town, east of Ramallah, "deliberately rammed the two Israelis while at the junction outside Ofra colony".
"Security poles that had been set up near the bus stop due to a previous ramming attack that had taken place at that bus stop prevented injury to other civilians who were standing at the bus stop", he recounted.
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The military gave no details about the suspect, but photographs showed the auto had Palestinian licence plates.
A man in his twenties was killed in the attack, and a 19-year old injured.
The death brings to 39 the number of Israelis killed in a wave of Palestinian street attacks, in which two American tourists also died, that began in October 2015.
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Pictures published by Israeli media showed a vehicle with Palestinian licence plates, which had mounted the pavement, surrounded by soldiers.
The auto ramming is the first fatal attack on Israelis since January 8, when a Palestinian killed four soldiers in a Jerusalem truck-ramming attack. Others have been killed in clashes with Israeli troops.
"There is no safety for the occupation army or settlers as long as they deny our rights, occupy our land, and attack our people and its holy sites", he added.
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It is located in east Jerusalem, occupied by Israel in 1967 and later annexed, and is central to the Israeli-Palestinian conflict.