Israeli Prime Minister Benjamin Netanyahu held the Palestinian Authority responsible for their wellbeing, but Palestinians baulked at the idea they were to blame for the disappearance inside an Israeli-controlled area of the West Bank.
The abductions come as Israel piles pressure on a new Palestinian government, formed early last week under a reconciliation deal between the Palestine Liberation Organisation and Israel foe Hamas.
The three, all students at a Jewish seminary, went missing late Thursday as they were hitchhiking between Bethlehem and Hebron.
He said the search is being carried out in coordination with security forces from the Palestinian Authority, and that "tens of Palestinians" have been arrested in the process.
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He added that substantial reinforcements had been brought in, including special forces and an airborne brigade, to participate in the search around Hebron, in the southern West Bank.
Israeli Defence Minister Moshe Yaalon was also on his way to the site of the disappearance to discuss the situation, army radio said.
A rocket was fired from Gaza into Israel early today without causing any casualties or damage, the army said.
In response, Israel carried out air strikes on southern Gaza "hitting a site of terrorist activity and a weapons depot," an army statement said.
Hamas said Apache gunships had fired on a training camp of its armed wing in Khan Yunis and empty ground in Rafah, on the Egyptian border, without causing any casualties.
Kerry also telephoned Abbas, a Palestinian source said.
A spokesman for the Palestinian Authority's security services, General Adnan al-Damiri, called Netanyahu's suggestions "mad.