Benjamin Netanyahu said an “intensive operation” is under way to find the two 16-year-olds and one 19-year-old.
The three seminary students went missing near an Israeli settlement north of Hebron as they were returning from evening lessons.
Palestinian officials say they are co-operating with the search.
“Our children were kidnapped by a terror group,” Benjamin Netanyahu said.
“There is no doubt about that.”
The teenagers have been identified as Naftali Frenkel, Gilad Shaar – both 16 – and Eyal Yifrach, 19.
They were last seen in the area of Gush Etzion, a bloc of Jewish settlements located between Jerusalem and the predominantly Palestinian city of Hebron.
The Israeli army says it is conducting house-to-house searches in the West Bank.
The search is being seen as the biggest strain on relations between the two sides since a Palestinian unity government was announced in April.
Benjamin Netanyahu has already said he holds the Palestinian Authority responsible for the teenagers’ wellbeing.
In response, Palestinian officials have pointed out that the three went missing in an area under full Israeli control.
Israel has arrested at least 12 people in the Hebron area, they say.
In an earlier statement on the operation, the Israeli army pointed to the 2006 kidnapping of Israeli soldier Gilad Shalit and said the three may have been taken to be traded for Palestinian prisoners held by Israel.
Sgt. Gilad Shalit was freed in 2011 after Israel and the Islamist movement Hamas agreed a deal under which more than 1,000 Palestinians were released.
In April, Israel suspended crisis-hit peace talks with the Palestinians when a Hamas-backed Palestinian unity government was announced.
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