Search continues for kidnapped students, who have now been named; PM: Palestinian Authority responsible for their safety.

Prime Minister Binyamin Netanyahu has confirmed that the three yeshiva boys who went missing Thursday were indeed kidnapped by terrorists.

"Our boys were kidnapped by a terrorist organization. There is no doubt about that," the Prime Minister said in an official statement after an emergency security meeting with the Defense Minister and IDF Chief of Staff, adding that an intensive effort is being made to avoid the kidnapped students being smuggled out the Hevron area.

"We are in the midst of a widespread operation to locate and bring back the three young yeshiva students. I spoke with their parents, and I told them that we are doing everything possible and more to bring back their boys, who are also our children."

Netanyahu reiterated that he holds the Palestinian Authority responsible for the boys' safety.

"I have ordered... to demand from the Palestinian Authority, headed by Abu Mazen (Abbas) - from whose territory the kidnappers came - to do whatever necessary to help the hostages get home safely," Netanyahu said. "That is the Palestinian Authority's responsibility."

On Friday a spokesman rejected the notion that the PA was responsible, but PA chief Mahmoud Abbas in a statement said he was ready to aid Israel in locating the boys.

IDF Chief of Staff Lt. Benny Gantz also issued a statement Saturday night.

"The IDF has been operating over the past two days in every place that needs investigating [for the return of the missing teens], in an operation which is widening in scope," he said.

"We'll keep an eye on what is happening in other arenas," he continued, vowing to continue the search "with responsibility and determination."

At the same time, the IDF Spokesperson's Office also issued a statement via its official Twitter account that the three were kidnapped by Palestinian Arab terrorists.

"We can confirm that the 3 missing Israelis in Judea & Samaria were kidnapped by #Palestinian terrorists," the IDF Spokesperson's Office tweeted Saturday night.

'Assumption is they are still alive'

The search continues for the trio, who were kidnapped as they were hitchhiking in Gush Etzion, south of Jerusalem, with security officials saying they fear for the lives of the missing boys.

Defense Minister Moshe Yaalon has vowed not to rest until the boys are found and those responsible for their kidnapping are hunted down. He told reporters Saturday that authorities are working on the assumption that they are still alive.

"Because we have no information to the contrary, we are assuming that they are still alive," he told reporters.

A gag order on naming the trio has now been lifted. They have been identified as Eyal Yifrah, 19, from Elad; Naftali Frenkel, 16, from Nof Ayalon; and Gilad Sha'ar, 16, from Talmon.

The three missing students Courtesy of the families

Security services have been scouring the Hevron region since Friday.

The IDF has closed the main crossings into the Gaza Strip to prevent the teenagers from being smuggled into the territory, where the Islamist Hamas movement remains dominant despite the formation of the Palestinian unity government.

Over the weekend, synagogues across Israel conducted special prayers for the boys, saying Psalms (Tehilim) 121 and 130.

According to AFP, both Hamas and the Palestinian Authority (PA) have denied responsibility for the attack, claiming that the kidnapping could not have been carried out by Palestinian Arabs since Gush Etzion is completely under Israeli control.

It is a somewhat weak claim given that all Palestinian terrorist attacks take place in areas under Israeli control, since no Jews live under Palestinian Authority control.

Those statements appear to be a desperate attempt to deflect criticism, as Israeli Prime Minister Binyamin Netanyahu has already blamed the recent unity deal between Hamas and Fatah for emboldening terrorists.

Speaking on Friday evening with U.S.Secretary of State John Kerry, Netanyahu told Kerry that the boys’disappearance was directly related to the Palestinian Authority signing a reconciliation pact and forming a unity government with the Hamas terrorist group.

"What is happening on the ground since Hamas was added to the government is a deterioration of the situation. This is the direct result of allowing a murderous and racist terrorist organization into the government," Netanyahu told Kerry, according to Channel 2 News.

Netanyahu also reiterated that Israel holds PA Chairman Mahmoud Abbas responsible for the three students’ disappearance and possible kidnapping.

No information has been released as to who authorities which group is holding them.

A statement in Arabic made its way around social media over the weekend claiming ISIS, the extremist group based in Iraq and Syria, was responsible for the attack, but its authenticity could not be confirmed and appears highly unlikely since the group does not have a known presence in Judea and Samaria.