Representatives of several terror group in the Gaza Strip, including Hamas, on Tuesday denied involvement in last Thursday’s kidnapping of three Israeli teenagers, but stressed that they support any effort to release Palestinian prisoners jailed by Israel.

In a press conference held in the Gaza Strip, members of Hamas and a number of other terror organizations claimed they were not responsible for the Thursday abduction of Eyal Yifrach, 19, Gil-ad Shaar, 16 and Naftali Frankel, 16, south of Jerusalem, but said that on principle, they reserve the right to kidnap Israelis in order to secure the release of Palestinians held in Israeli security facilities.

In a televised statement to the press, a gun wielding, masked Hamas operative praised the kidnapping, and added the group would not hesitate to retaliate against Israel if an IDF crackdown on the group in the West Bank continued.

“We are one, and the West Bank performs its role in the Holy war against the enemy,” the Hamas member said.

Islamic Jihad representatives did not take part in the press conference, Ynet reported.

Israel has blamed Hamas for the kidnapping, carrying out some 200 arrests of the group’s members across the West Bank. A Hamas statement called the accusation against it “stupid” on Sunday, and officials are looking to raise doubts over the fact that there was a kidnapping at all.

Hamas officials asserted Tuesday that Israel had staged the kidnapping, in an attempt to dismantle the newly established Palestinian unity government and weaken Hamas influence in the West Bank, Channel 2 reported.

IDF soldiers in Hebron on June 17, 2014. (photo credit: AFP Photo/Hazem Bader)

IDF soldiers in Hebron on June 17, 2014. (photo credit: AFP Photo/Hazem Bader)

In a statement released earlier Tuesday on behalf of Hamas’s office in Hebron, where the IDF’s search for the teens has been focused, the organization declared it would not capitulate to Israeli pressure and the numerous arrests of its members.

“You will not break us,” it read.

“We’ve been through attacks like these by Israel in the past, but we withstood them,” the Hebron statement said, according to Channel 10. “The Hamas movement is not a movement of dozens, hundreds, or thousands, but is an entire stream. The arrest of hundreds of our sons won’t stop us, won’t change our path, and won’t separate us from our commitments and obligations to the Palestinian nation.”

Three kidnapped Israeli teens, from L-R: Eyal Yifrach, 19, Naftali Frankel, 16, and Gil-ad Shaar, 16. (photo credit: courtesy)

Three kidnapped Israeli teens, from L-R: Eyal Yifrach, 19, Naftali Frankel, 16, and Gil-ad Shaar, 16. (photo credit: courtesy)

The Hebron statement also urged Palestinians to continue efforts to free the hunger-striking administrative detainees in Israel, and called on the Palestinian Authority to release all the Hamas political prisoners in its custody.

“We call on all factions to unite and stand against the Zionist attack and maintain cohesion,” it said.

The statements came hours after the security cabinet announced it would worsen conditions for about a thousand Hamas prisoners in Israeli prisons.

The three teenagers were kidnapped last Thursday night in the West Bank. They were last seen at a hitchhiking post in the Etzion Bloc of settlements south of Jerusalem at around 10:25 p.m.

The Israeli government has pointed the finger at Hamas and said that it holds the Palestinian Authority responsible for their well-being.

General Officer of the IDF’s Central Command Nitzan Alon said Tuesday that Hamas leaders were “frantic,” and that the army had over the past few days dealt the organization a severe blow.

“IDF forces struck at the oxygen of terrorism, and Hamas leaders feel the damage and understand the message,” he said, Ynet reported.

IDF activity on Tuesday expanded across all of the West Bank in an effort to hamstring Hamas’s financial and operational infrastructure, an official said. Israel’s security cabinet discussed further steps Monday, including the possible deportation of Hamas leaders from the West Bank to the Gaza Strip, where Hamas is in control.