* Bodies of missing teens found in West Bank field
* Israel blames Hamas for abduction, strikes in Gaza
* Israeli security cabinet meets to decide scope of future action (Adds security cabinet meets, Netanyahu quote)
By Ori Lewis
MODI'IN, Israel, July 1 (Reuters) - Tens of thousands of mourners joined in an outpouring of national grief on Tuesday at the burial of three Israeli teenagers whose kidnapping and killing Israel blamed on the Palestinian Islamist group Hamas.
In his eulogy at the cemetery in the centre of the country, President Shimon Peres, a usually dovish elder statesman, echoed official vows to punish Hamas.
"I know that the murderers will be found. Israel will act with a heavy hand until terror is uprooted," he said at the ceremony in Modi'in, a town between Jerusalem and Tel Aviv.
Israel bombed dozens of sites in the Gaza Strip on Tuesday, wounding two Palestinians, as it struck at Hamas a day after finding the bodies of the three youths in the occupied West Bank, not far from where they went missing while hitchhiking on June 12.
After the funeral, Israel's security cabinet convened for a second time in as many days. Officials said ministers were split on Monday on the scope of any further action in the coastal enclave or in the West Bank. The United States and regional power-broker Egypt urged restraint.
Prime Minister Benjamin Netanyahu has pledged Hamas would pay for the slayings and reiterated before Tuesday's meeting that Israel "must strike hard at Hamas people and infrastructure in the West Bank" and would weigh further attacks to prevent rocket fire from Gaza on southern Israel.
Netanyahu vowed to strike at anyone involved in the kidnappings. "We will get them, even if it takes time," he said.
Defence Minister Moshe Yaalon said "Hamas's leaders and members should know that the blood of whoever dares strike at the citizens of Israel is forfeit. They should know that we will pursue them wherever they are and hit them hard."
Just before the funeral, a recording of a furtive cellphone call one of the abducted teens made to a police emergency number was broadcast on Israeli television stations.
"They've kidnapped me," the youngster said. Shouted orders in Arabic-accented Hebrew - "head down, head down" - and the sound of what appeared to be muffled gunfire followed before the call ended.
ATTACKS ON GAZA
The military said aircraft attacked 34 targets in Gaza, mostly belonging to Hamas, but did not link the strikes to the abductions. The military cited 18 Palestinian rockets launched against Israel from Gaza in the past two days.
Palestinian medics said two people were slightly wounded.
The Islamist group has neither confirmed nor denied involvement in the disappearance of the students nor in the cross-border rocket salvoes from Gaza.
Two more rockets fired from Gaza struck inside Israel on Tuesday evening, causing no casualties, the military said.
Before their joint burial in the Israeli city of Modi'in, funeral services were held outside the homes of Gil-Ad Shaer and U.S.-Israeli national Naftali Fraenkel, both 16, and Eyal Yifrah, 19.
"There hasn't been a show of unity like this in Israel for years," Fraenkel's father, Avraham, said at the service as he stood facing the body of his son, which was draped in an Israeli flag.
Israeli television and radio stations interrupted regular programming to broadcast the funeral, which began more than an hour late as large crowds streamed into the cemetery.
"This shows unity among the people, but unfortunately it only happens in times of sorrow," said one mourner, Shalom Balas, 47, a lawyer from Modi'in.
SECURITY CABINET DIVISIONS
At Monday's security cabinet meeting, the army proposed "considered and moderate actions" against militants in the West Bank, officials said. Any sustained campaign there could undermine U.S.-backed Palestinian President Mahmoud Abbas.
But the cabinet did not agree on a future course of action at that session, officials said.
In Gaza, Hamas spokesman Sami Abu Zuhri warned Israel against going too far.
"The response of the resistance has been limited, and Netanyahu must not test Hamas's patience," said Abu Zuhri, whose group's arsenal includes rockets that can reach Tel Aviv.
Netanyahu seized on the abduction to demand Abbas annul a reconciliation deal he reached with Hamas, his long-time rival, in April that led to a unity Palestinian government on June 2.
An Arab diplomat familiar with Egyptian mediation between Israel and the Palestinians said Cairo, echoing Washington, expected the Netanyahu government to tread carefully.
"I don't believe Israel is ready, just yet, to change the status quo," he told Reuters on condition of anonymity. "It can punish those who did the crime, but should not get out of control with civilians who had nothing to do with the crime."
In the West Bank on Tuesday, Israeli troops shot dead a Palestinian who a military spokeswoman said threw a grenade at soldiers attempting to detain a militant. A Palestinian witness said the 19-year-old killed by the troops was a passerby.
The men Israel has accused of carrying out the abductions are still at large.
Troops set off explosions late on Monday in the family homes of the alleged abductors in the West Bank town of Hebron, blowing open a doorway in one, an army spokeswoman said. The other property was on fire after the blast. Soldiers who arrested one of the suspect's father and brothers ordered the inhabitants of the dwellings to leave before the detonations.
"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 to her home.
Hamas has been rocked by the arrest of dozens of its activists in an Israeli sweep in the West Bank over the past three weeks during the 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
Abbas condemned the abduction and pledged the cooperation of his security forces. That drew criticism from Hamas and undercut 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 Dan Williams, Maayan Lubell and Allyn Fisher-Ilan in Jerusalem, Nidal al-Mughrabi in Gaza and Noah Browning and Ali Sawafta in Hebron; Writing by Jeffrey Heller; Editing by Tom Heneghan, Larry King)