(CNN) -- Many of Israel's 8 million citizens were in mourning Tuesday as three teens, whose bodies were found Monday, were to be buried.
At a large funeral, Prime Minister Benjamin Netanyahu will deliver the eulogy, his office announced. President Shimon Peres will attend as well.
Processions for each of the three boys -- Eyal Yifrach, 19; Gilad Shaar, 16; and Naftali Frankel, a 16-year-old dual U.S.-Israeli citizen -- will meet up at Modi'in cemetery, Israeli media reported.
"I'm holding his picture and I see his smile," said Leehy Shaar, Gilad Shaar's aunt. "He's so young and innocent. ... It's just too sad to even imagine."
Their killings, which Israel blames on Hamas, galvanized the nation and drew condemnations across the globe.
Overnight, Israel stepped up airstrikes on Gaza. The military said it struck 34 terror infrastructure targets after 18 rockets had been fired into Israel since Sunday evening.
Palestinian medical sources said a Palestinian man was killed in the West Bank. Official Palestinian news agency Wafa said the 21-year-old was killed "in cold blood." The Israeli military said a Hamas-affiliated terrorist hurled a grenade toward soldiers, who responded to the "immediate threat and opened fire towards the terrorist."
"Vengeance for the blood of a small child, Satan has not yet created. Neither has vengeance for the blood of three pure youths who were on their way home to their parents who will not see them anymore," Netanyahu told his Cabinet. "Hamas is responsible and Hamas will pay. May the memories of the three boys be blessed."
"They were abducted and murdered in cold blood by human animals," he said. He told the boys' families: "The entire nation weeps with you."
Hamas, the militant Islamic organization that controls Gaza, denied it was behind the abductions. If Netanyahu "brings a war on Gaza," the group warned, "the gates of hell will open to him."
Palestinian news agency Ma'an reported Tuesday that a little-known group called Ansar as-Dawla al-Islamiya (Supporters of the Islamic State) had claimed responsibility for the killings and threatened to "slaughter" the Palestinian Authority.
CNN could not independently verify the claim.
The Israel Defense Forces has named two suspects, saying Marwan Kawasme and Omar Abu Aysha are the "Hamas terrorists who kidnapped" the boys. Their West Bank homes were destroyed overnight.
The three Israeli teenagers disappeared 19 days ago while trying to hitchhike home from school in the West Bank. On Monday, volunteers from an Israeli settlement discovered their bodies in an open field not far from Hebron, a southern West Bank city.
The Palestinian Cabinet on Tuesday said Israel has killed 12 Palestinians since Israel began military operations to find the teens on June 13. The Cabinet called on other nations to stop what it said were "Israel's illegal measures."l
The Cabinet didn't release details on the 12 dead. CNN reported earlier, citing Palestinian medical sources, that at least one man died from a heart attack during a raid on his West Bank home last month; at least five were killed in clashes with the Israeli military; and two men accused by the Israeli military of being involved in recent rocket attacks were killed in an airstrike last week in Gaza.
"Deeply saddened and outraged by news of the tragic murders," New York Mayor Bill de Blasio tweeted. "NYC mourns them together with their families." Frankel's family comes from New York. Gov. Andrew Cuomo tweeted that he was "deeply shocked and saddened" and added, "Our thoughts & prayers are with their families and the state of Israel."
In Washington, the top Republican and Democrat on the House Middle East subcommittee issued a warning to Palestinian Authority President Mahmoud Abbas, who recently reached the latest in a string of unity government agreements with Hamas. "If it is determined that Hamas is behind this horrific tragedy, (Abbas) must immediately break up the unity agreement between Fatah and Hamas, a U.S. designated foreign terrorist organization," Reps. Ileana Ros-Lehtinen, R-Florida, and Ted Deutch, D-Florida, said in a joint statement.
"No words can adequately express the sorrow and sadness we feel for the families of Gilad, Naftali and Eyal, the people of Israel and the entire Jewish community worldwide," they said. "This is a day of tragedy and mourning; the world has lost three beloved sons, friends, and beautiful souls who were taken from us too early, but will forever live on in our hearts and minds. We will continue to support the Government of Israel in its efforts to bring the perpetrators to justice, and we offer the people of Israel our deepest and most heartfelt condolences as we grieve with them."
Mark Regev, a spokesman for Netanyahu, suggested Monday that the Palestinian Authority also bore some responsibility for what happened.
"It's clear that the terrorists came from areas under Palestinian Authority control and returned to territories under Palestinian Authority control," he said.
Abbas, who has condemned the teens' abduction, called an emergency meeting of his own. The Palestinian leadership is expected to meet Tuesday to discuss the developments.