The names of the three missing teenagers were cleared for publication on Saturday afternoon. The teens are Eyal Yifrah, 19, from Elad, Gil-Ad Shaer, 16, from Talmon and Naftali Frenkel, 16, from Nof Ayalon. Both Frenkel and Shaer study at the Makor Chaim yeshiva in Kfar Etzion, while Yifrah studies at the Shavei Hevron yeshiva.
Earlier, Defense Minister Moshe Ya'alon said the working assumption was that the three students, who are feared kidnapped, are alive.
In the first public statement the defense minister gave since the three teens disappeared, he said: "As long as we don't know differently, our working assumption is that they are alive."
"We are in the midst of an intelligence and operational effort. A considerable number of forces have been deployed to the Judea and Samaria District, specifically to the Hebron area. They are making arrests - some done during the night - and searching the area," Ya'alon told reporters.
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Ya'alon said all security forces were working together to find the three students, and admitted that while the Shin Bet managed to thwart over 30 kidnapping plots in 2013, and 14 so far in 2014,"it seems that this event got in under our radar."
Following a situation assessment, the defense minister instructed the Etzion and Binyamin territorial brigade commanders to increase the intelligence effort in their areas as well. The meaning of this move is that the wave of arrests will be expanded beyond Hebron.
The IDF deployed over 2,000 soldiers to the Hebron area. Three battalions from the Paratroopers Brigade and another battalion from the Kfir Brigade were sent to the West Bank to deal with the possible break out of violent riots.
At the moment, the newly-deployed forces have been stationed at a training base a short distance away from the Judea district and would be called in to impose a closure on the Palestinian-controlled areas of the West Bank if necessary.
The IDF decided not to place checkpoints around Hebron for the time being, to avoid disrupting the Palestinians' day-to-day life. Movement in and out of Hebron and its surrounding area is continuing as usual at the moment.
A senior military official said special forces are combing through the southern West Bank and that progress has been made by intelligence units but would not elaborate.
"We need more boots on the ground to deal with this serious development. We need to be able to track them down, we need to use all of the capabilities at our hands in order to bring this to a quick end," the senior official said.
He also said Israel was working with the Palestinian Authority to try to locate the teens.
Overnight, IDF soldiers arrested at least 12 Hebron area residents, including two women, according to Palestinian officials. Locals said some of those detained were involved in car businesses like repair garages - indicating that the investigation was focusing on tracking down potential means of transport for a kidnapping.
Two of the Palestinians arrested were previously released from Israeli jail, identified by Palestinian news agency Ma'an as Iyad Abdul-Nabi Shabana and Dirara Abu Munshar.
Palestinian witnesses said the troops were also confiscating video from privately owned security cameras in Hebron and had prevented around 300 residents from leaving the area.
Three different claims of responsibility for the purported kidnapping have emerged in the West Bank, though it's not clear if any are authentic.
In one leaflet, a group portraying itself as a branch of an al-Qaeda splinter group said it kidnapped the three to avenge the killing of three fighters in a clash with Israeli security forces earlier this year. Another statement was purportedly issued by the Al Quds Brigades, the military wing of the Islamic Jihad group.
Reuters and Associated Press contributed to this report.