"Hamas is responsible and Hamas will pay."
After several hours the cabinet session ended without further public comment and public radio said ministers would reconvene on Tuesday evening.
A senior Hamas official warned Israel against reprisals, saying it would open "the gates of hell".
The discovery of the three bodies in a field in the southern West Bank came 17 days after the youngsters disappeared, triggering a huge manhunt during which five Palestinians were killed and more than 400 arrested.
Two Hebron Hamas men named by Israel as prime suspects -- Marwan Qawasmeh and Amer Abu Eishe -- remain at large but Palestinian witnesses said troops blew up their homes early Tuesday.
The Israeli roundup -- mainly of people linked to Hamas -- brought a wave of rocket attacks against southern Israel by militants in the Gaza Strip, answered in turn by Israeli air strikes.
The latest round began around 1:00 am Tuesday (2200 GMT Monday) with a rocket slamming into open ground in the Negev desert region.
An army statement said nobody was hurt.
Shortly afterwards the Palestinian interior ministry reported around 30 Israeli air strikes on deserted militant training sites across Gaza but there was no immediate word of casualties.
The ministry said that among targets hit by F-16 fighters were bases of Hamas and Islamic Jihad.
- 'Found at the end of the world' -
The youngsters' bodies were found in the southern West Bank near the town of Halhul, some 10 minutes drive from the roadside where they were last seen hitchhiking.
"During the search for Eyal Ifrach, Gilad Shaer and Naftali Frankel, the IDF discovered three bodies," the Israeli army said on Twitter.
Army spokesman Lieutenant Colonel Peter Lerner refused to comment on the cause of death.
He told reporters the bodies were being transferred for formal forensic identification.
"We have informed the families but final identification is pending."
One of the civilian volunteers involved in the search told army radio the bodies had been found under a pile of branches and stones in a remote area.
"Today, during a sweep with the army, one of the guys spotted something unusual, they started to move branches and stones and found the bodies," said volunteer Benny Truper.
"It was a very isolated area, more or less at the end of the world."
US President Barack Obama on Monday condemned the killings and warned against actions that could further "destabilise" the situation, amid the threats of retaliation against Hamas.
"The United States condemns in the strongest possible terms this senseless act of terror against innocent youth," Obama said in a written statement.
British Prime Minister David Cameron slammed an "inexcusable act of terror" and vowed to stand with Israel as it seeks justice, while French President Francois Hollande denounced the "cowardly murder" of the teens.
- Hamas warns Israel -
Following the teenagers' disappearance, Israel launched a vast search and arrest operation, which also sought to lay waste to Hamas's West Bank network.
More than 400 Palestinians were arrested, two thirds of them Hamas members, and another five people killed in clashes sparked by the campaign, dubbed Operation Brother's Keeper.
But Hamas on Monday warned Israel against any further punitive action against the Islamist movement.
"If the occupiers carry out an escalation or a war, they will open the gates of hell on themselves," Hamas spokesman Sami Abu Zuhri told AFP.
Hamas has dismissed the Israeli allegations as "stupid" with Abu Zuhri accusing Israel of fabricating the kidnapping as an excuse to crack down on it.
"The occupation is trying to use this story to justify its extensive war against our people, against resistance and against Hamas," he charged.
President Mahmud Abbas convened an emergency meeting of the Palestinian leadership to discuss the latest developments.
Abbas has come under massive Israeli pressure to renounce a reconciliation agreement with Hamas under which a merged administration for the West Bank and Gaza was formed in early June for the first time in seven years.
Pope Francis, who last month visited Israel and the West Bank, called the killing "an abominable crime."
"This is a serious obstacle on the path to peace for which we must continue to pray and continue to be involved," a Vatican statement quoted him as saying.