Prime Minister Benjamin Netanyahu blamed the Palestinian Authority for the Thursday night disappearance of the teens, one of them a U.S. citizen.
"Our children were kidnapped by a terror group," he said. "There is no doubt about that."
Palestinian officials say they are assisting Israeli forces, who examined surveillance footage Saturday and arrested more than a dozen Palestinians.
Netanyahu said an "intensive operation" was underway to prevent the teens from being taken to the Gaza Strip or elsewhere.
Israeli security forces searched the West Bank for a second day Saturday for the three students of a Jewish seminary.
"I hope that these efforts will lead us as quickly as possible to the missing in order to rescue them alive," Defense Minister Moshe Yaalon said. "As long as we don't know otherwise, our working assumption is that they are alive."
The Israeli military identified the trio as Naftali Frenkel, 16, Gilad Shaar, 16, and Eyal Yifrach, 19. Israeli television station Channel 10 said Frenkel was a U.S. citizen.
Defense officials said they believe the three students were kidnapped near Hebron by Palestinian militants who want to trade them for jailed comrades.
The teens' disappearance is the first serious incident to strain relations with Israel since the formation of a Palestinian unity government this month led by Western-backed President Mahmoud Abbas and backed by the Islamist militant group Hamas.
An al-Qaeda offshoot of the Sunni extremists sweeping through Iraq claimed responsibility for abducting the teens as retaliation for the killings of three militants by Israeli forces in November, Haaretz reported.
Prime Minister Benjamin Netanyahu blamed Hamas, which recently joined the Palestinian government after U.S.-brokered peace talks failed. The Palestinian Authority denied involvement.
Secretary of State John Kerry spoke with Netanyahu and Palestinian Authority President Mahmoud Abbas, the State Department said.
"Secretary Kerry has … spoken to President Abbas to urge him to do everything possible to assist in the effort to find them. President Abbas assured him that he is doing so," a spokesman said.
An extremist Salafist group known as Dawlat al-Islam distributed pamphlets claiming responsibility for the abductions. The organization is linked to ISIS.
The State Department has issued a travel warning for Israel, the West Bank and the Gaza Strip.
Contributing: The Associated Press
