Prime Minister Benjamin Netanyahu blamed the Palestinian Authority for their disappearance without elaborating, saying he held the government responsible for their safety.
Palestinian authorities could not be immediately reached for comment.
Two Israeli defense officials said authorities believed the teens likely were kidnapped by Palestinian militants, without elaborating. They spoke on condition of anonymity as they were not allowed to speak with journalists.
Brig Gen Motti Almoz, a military spokesman, said that the military and intelligence forces were involved in the search for the missing teens.
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Tsuri Tsuf, a spokesman for a settlement where one of the teens is from, told Israel's Channel 10 television that his community was "greatly worried" and gathered to pray for the safety of the youths.
The station reported the teenagers hitched a ride the night before from their Yeshiva, or religious seminary, and had not been seen since.
It reported that one of the teenagers called the police to say they had been kidnapped. The station did not say where it obtained the information.
If Palestinians abducted the teens, it would be the first serious incident to challenge relations with Israel since the formation of a Palestinian unity government earlier this month, led by President Mahmoud Abbas' Fatah party and backed by the Islamic militant group Hamas.
Hamas frequently calls for the abduction of Israelis. The Israeli military has said it has foiled multiple Palestinian kidnapping attempts in recent years and warns soldiers and civilians not to accept rides from strangers. Despite the warnings, hitchhiking remains common in Israel.