* Bodies found in West Bank field
* Israel blames Hamas for abduction
* Netanyahu consults with security cabinet
* Obama condemns killings, urges restraint (Adds Israeli air strikes, details of security cabinet meeting)
By Jeffrey Heller
JERUSALEM, July 1 (Reuters) - Israel bombed dozens of sites in the Gaza Strip on Tuesday, striking at Hamas after finding the bodies of three missing teenagers whose abduction and killing it blames on the Palestinian Islamist group.
Israel's security cabinet, which held an emergency session late on Monday and was due to meet again on Tuesday, was currently split on the scope of any further action in the coastal enclave and the occupied West Bank, officials said.
Prime Minister Benjamin Netanyahu had promised Hamas would pay after the discovery of the three Jewish seminary students' bodies under a pile of rocks near the West Bank city of Hebron on Monday.
The military said aircraft attacked 34 sites, mostly belonging to Hamas, though its statement did not link the strikes to the abductions.
Instead, it cited 18 Palestinian rocket launched against Israel from Gaza in the past two days which Israeli officials have said Hamas carried out.
The Islamist group has neither confirmed nor denied Israel's allegations about its role in the disappearance of the students as they hitchhiked near a Jewish settlement on June 12.
At the security cabinet meeting, the army proposed "considered and moderate actions" against militants in the West Bank in response to the teenagers' deaths, said officials. Any sustained campaign there could undermine Western-backed Palestinian President Mahmoud Abbas.
But the cabinet did not agree on a future course of action at that session, officials added.
In the West Bank on Tuesday, an Israeli military spokeswoman said troops opened fire at a man, identified by Palestinian officials as Yousouf Ibrahim abu Zagha, 19, who threw a grenade at soldiers who were attempting to arrest a militant in the Jenin refugee camp.
The kidnapping appalled Israelis who rallied behind the youngsters' families in a display of national unity.
"They were kidnapped and murdered in cold blood by beasts ... Hamas is responsible and Hamas will pay," Netanyahu said in a statement on Monday.
The funerals of Gil-Ad Shaer and U.S.-Israeli national Naftali Fraenkel, both 16, and Eyal Yifrah, 19 were due to take place later on Tuesday.
The teens, who attended a religious school in a Jewish settlement, had apparently been shot soon after being taken, officials said. Two of the youths lived in Israel.
The men Israel has accused of carrying out the abductions are still at large. Israeli media said the break in the case came after their relatives were interrogated.
Troops late on Monday set off explosions in the family homes of the alleged abductors, blowing open a doorway in one, an army spokeswoman said. The other property was on fire after the blast. Neighbours said both houses were empty.
"This kind of act is a sin, whether you're a Muslim or Jew. They've scared the kids so much," Um Sharif, the mother of one of the alleged kidnappers said about the damage caused to her home. She said she did not believe her son had been involved.
Hamas has been rocked by the arrest of dozens of its activists in an Israeli military sweep in the West Bank over the past three weeks during a search for the teenagers that Israel said was also aimed at weakening the militant movement.
Up to six Palestinians died as a result of the Israeli operation, local residents said
After news of the teenagers' deaths, condolence messages and condemnation of the killings poured in from foreign leaders.
"The United States condemns in the strongest possible terms, this senseless act of terror against innocent youths," President Barack Obama said in a statement. "I also urge all parties to refrain from steps that could further destabilise the situation."
Netanyahu seized on the abduction to demand Abbas abrogate a reconciliation deal he reached with Hamas, his long-time rival, in April that led to a unity Palestinian government on June 2.
Abbas condemned the abduction and pledged the cooperation of his security forces, drawing criticism from Hamas and undercutting his popularity among Palestinians angered by what they saw as his collusion with Israel.
Hamas, which has maintained security control of the Gaza Strip since the unity deal, is shunned by the West over its refusal to renounce violence. The group has called for Israel's destruction, although various officials have at times indicated a willingness to negotiate a long-term ceasefire.
(Additional reporting by Maayan Lubell and Ori Lewis in Jerusalem, Nidal al-Mughrabi in Gaza and Noah Browning and Ali Sawafta in Hebron; Editing by Janet Lawrence, Mohammad Zargham and Cynthia Osterman)