Updated

A terror group abducted the three teens missing from the West Bank, Israel's prime minister said Saturday, as soldiers combed the rocky terrain and searched homes to try and find them.

Prime Minister Benjamin Netanyahu again blamed the Palestinian Authority for the Thursday night disappearance of the teens, one of them a U.S. citizen. Palestinian officials say they are assisting Israeli forces, who poured over 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.

"Our children were kidnapped by a terror group," he said. "There is no doubt about that."

The Israeli military identified the teens as Naftali Frenkel, 16, Gilad Shaar, 16, and Eyal Yifrach, 19. Israeli television station Channel 10 named Frenkel as the U.S. citizen that officials earlier mentioned.

Their kidnapping is the biggest abduction by militant groups in recent memory in the West Bank.

Israeli-Palestinian tensions already were strained at the time of Thursday's kidnapping, in part because of the recent formation of a Palestinian unity government that has the backing of the Islamic militant group Hamas.

Israeli Defense Minister Moshe Yaalon said Saturday that Israel has thwarted more than a dozen kidnapping attempts by Palestinian militants so far this year.

"It appears this event slipped under our radar, but we will not rest until we free the youths and put our hands on the terrorists who are responsible for this operation," Yaalon said.

"As long as we don't know otherwise, our working assumption is that they are alive," he said.

Hamas, branded a terror group by the West for its attacks aimed at civilians, has been involved in kidnappings of Israelis in the past. The group routinely claims responsibility if involved in an attack, but has not claimed taking the teens.

Palestinian officials also rejected Israel's attempts to blame Abbas, noting that Israel retains overall security control in the West Bank.

Despite the charged rhetoric, Palestinian security forces were cooperating with Israeli counterparts in trying to find the teens, a Palestinian official said.

Abbas has said security coordination in the West Bank between Israel and the Palestinians, usually aimed at tracking down Islamic militants, will continue despite the unity government.

Meanwhile, three different claims of responsibility emerged in the West Bank, though it's not clear if any were authentic.

In one leaflet, a group portraying itself as a branch of an al-Qaida splinter group said it kidnapped the three to avenge the killing of three fighters by Israeli security forces earlier this year.

Hamas, along with other militant Palestinian groups, frequently call for the abduction of Israelis.

Israel's military has warned soldiers and civilians not to accept rides from strangers, but hitchhiking remains common.

An Israeli intelligence official said more than 50 kidnapping attempts were thwarted at various stages of execution in 2013 alone. Palestinians have kidnapped Israelis before but this would be the first time they abducted three civilians at the same time. The official spoke anonymously as he is not allowed to brief the media.

Israeli authorities clamped a partial gag order on the case.

Two of the three missing teens are from settlements in the West Bank, territory Israel captured from Jordan in the 1967 Mideast war and that Palestinians are demanding as part of their future state along with the Gaza Strip and east Jerusalem.

Hamas ruled Gaza for seven years, after violently taking over the territory from the Palestinian Fatah group in 2007, and remains the de facto power there despite the unity deal.