Israeli officials have convened an emergency security cabinet meeting, as Israeli troops set up roadblocks around Hebron. There have also been clashes with Palestinian protesters in the area.
Israeli media reported that the bodies of the three teenagers have been found.
Since their kidnapping, Israel has arrested more than 400 people, most apparently members of Hamas, and six Palestinians have been killed in clashes.
The teenagers – Gilad Shaar, Eyal Yifrach and Naftali Frenkel – disappeared two weeks ago after lessons at their religious studies institute near an Israeli settlement in the West Bank.
Israeli Prime Minister Benjamin Netanyahu publicly blamed Hamas for their disappearance (see video), but the group has denied the allegation.
Their kidnap resulted in thousands of Israeli soldiers and police scouring the West Bank and making scores of arrests, including that of Palestinian parliament speaker Aziz Dweik, a member of Hamas.
Israeli forces mounted, and have since sharply scaled back, a sweep through Palestinian towns and villages, mainly in and around the southern West Bank city of Hebron. Dozens of Hamas members have been detained.
Since the start of the Israeli operation, some 40 rockets have been fired into Israel from the Gaza Strip, the military said.
Mr Netanyahu has urged Palestinian President Mahmoud Abbas to abandon a reconciliation pact he sealed with Hamas in April, a deal that led to the creation on 2 June of a Palestinian unity government of technocrats.
Hamas has called for Israel’s destruction, although various officials have at times indicated a willingness to negotiate a long-term ceasefire.
After the disappearance, US Secretary of State John Kerry condemned what had happened, saying: “We are still seeking details on the parties responsible for this despicable terrorist act, although many indications point to Hamas’s involvement.”