People gather for a vigil for the three missing Israeli teens outside of the Israeli Consulate in New York City. (Spencer Platt/Getty Images/AFP)
Their deaths raised to four the number of Palestinians killed since the army began a massive search for the Israeli students who disappeared on June 12 while hitchhiking in the southern West Bank.
Israel accuses Hamas of kidnapping them, and has said the objective of "Operation Brother's Keeper" is to bring them home safe while dealing a crushing blow to the group's West Bank infrastructure.
So far, the army has arrested more than 340 Palestinians, around two thirds of them Hamas members.
Palestinian president Mahmud Abbas has denounced the abductions, but on Sunday said Israeli Prime Minister Benjamin Netanyahu should condemn the bloodshed triggered by the manhunt.
"I said the kidnapping was a crime, but does that justify the killing of... Palestinian teens in cold blood?" Abbas told Haaretz newspaper, referring to two young Palestinians who died this week.
"What does Netanyahu have to say about the killings? Does he condemn it?"
Abbas added: "I have no credible information that Hamas was behind the kidnapping."
Netanyahu, who insists Hamas abducted the youths, told a meeting of his cabinet that Israel has "unequivocal proof" and "soon this information will be made public".
Army spokesman General Motti Almoz said, meanwhile, that all information indicates the teens "are alive".
Netanyahu also said Abbas must show his good intentions by finding the youths and returning them home, and "by his willingness to dissolve the unity government with Hamas".
Israel has seized on the opportunity presented by the operation to try to rupture a reconciliation agreement between Abbas and Hamas, which saw the two sides recently agree on an interim government of independents, infuriating the Jewish state.
Also on Sunday, Netanyahu said Israel has "no intention of harming anyone", even if some Palestinians are being killed.
"But our forces are acting as necessary for self-defence, and from time to time, there are victims or casualties on the Palestinian side as a result."
President Shimon Peres, who recently prayed for peace alongside Abbas at the Vatican, praised the Palestinian for his "courage in condemning several times the abduction".
Abbas "is the best peace partner Israel ever had and we should not miss the opportunity of making peace with him," said Peres.
Abbas spokesman Nabil Abu Rudeina said the Palestinian leadership had begun efforts to call for "an urgent session of the UN Security Council to put an end to the ongoing brutal Israeli aggression".
He told AFP that they are appealing to international organisations to "protect" Palestinians from Israel's actions.
UN chief Ban Ki-moon, meanwhile, spoke to Netanyahu on Saturday voicing "deep solidarity" with the family of the missing Israeli boys, a UN statement said.
But he also "expressed concern over the increase violence, mass arrests and restriction of movement in the West Bank."
With the search now in its 10th day, troops shot dead Ahmed Fanawi, a 27-year-old mentally challenged man, in Nablus on his way to prayers, his family and medics said.
The army confirmed firing at a man who approached troops "in a threatening manner", saying he had failed to respond to warning shots.
But the military did not comment on the second reported fatality -- Mohammed Tarifi, 30, who Palestinian medics said was shot dead during clashes in central Ramallah that wounded five others.
Shortly after the soldiers left, Palestinians were seen hurling rocks at a police station in the city and smashing the windows of two police cars.
Later on Sunday, Israeli troops shot and wounded four Palestinians near Hebron, medics said.
The Israeli search has sparked growing Palestinian frustration with their own security forces who are cooperating in the hunt for the teenagers, in a move defended by Abbas as necessary.
Israeli rights groups sent a letter to Defence Minister Moshe Yaalon on Sunday, denouncing the crackdown which they branded "collective punishment" and a violation of basic rights.