One of the two had been evacuated in serious condition and later succumbed to his wounds, medical sources said.
Official Palestinian news agency Wafa identified the Palestinians shot dead as Saad Salah, 21, from the city of Jenin, and Aws Salame, 17, from the Jenin refugee camp.
A third Palestinian who was shot in the leg was in moderate condition, the medical sources said.
The Israeli army said soldiers shot toward "attackers" after "Palestinian gunmen opened fire at the forces and assailants hurled explosive devices at the forces" operating in the camp.
The army would not provide details on why the soldiers were in the area at the time.
Israel's military regularly carries out raids in the West Bank to make arrests or seize weapons.
Family members of Salah alleged later in the day as funerals were held for the two Palestinians that he had been "executed."
Mourners carried their bodies through the streets, their bodies wrapped in Palestinian flags.
"He returned to the camp and was surprised to see soldiers," Salah's brother Adnan Salah said, describing what the family said they had been told by witnesses.
A wave of unrest that broke out in October 2015 has claimed the lives of 277 Palestinians, 42 Israelis, two Americans, two Jordanians, an Eritrean, a Sudanese and a Briton, according to an AFP toll.
Israeli authorities say most of the Palestinians killed were carrying out knife, gun or car-ramming attacks.
Others were shot dead in protests and clashes, while some were killed in Israeli air strikes on the Gaza Strip.
The violence has greatly subsided in recent months.
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