The alleged bomber, Abd Allah Said Badran carried out the bombing operation to avenge the deaths of Palestinians killed by Israeli occupation forces, he said in a videotape message.
He also slammed the Palestinian Authority and described it as a unilaterally-ruling authority that merely follows US orders.
However, Islamic Jihad's leadership in Gaza denied any involvement in the bomb attack and said they were committed to the truce currently in force with the Israelis.
Late on Saturday, Israeli Defence Minister Shaul Mofaz accused Syria on Saturday of being implicated in the bombing in Tel Aviv in which four Israelis were killed.
Hizb Allah denial
Earlier in the day Lebanon's Hizb Allah denied involvement in the Saturday morning bombing that also wounded 53 people.
The explosion killed four people,
including the bomber
"Hizb Allah categorically denies the accusations of a supposed role by our movement in the Tel Aviv operation and considers them totally without basis," a statement from the group said.
"These accusations are part of a campaign of incitement against Hizb Allah led by the Hebrew state."
Israel has long accused Hizb Allah of funding attacks by groups in the West Bank and Gaza Strip.
An Israeli Foreign Ministry spokesman had earlier told Aljazeera that Hizb Allah wants to prevent the peace process from continuing.
"Hizb Allah wants to shake stability in the area and foil the mutual efforts to go forward in the peace process and the Palestinian Authority's efforts to ease the situation," he said.
When asked about possible involvement of Israeli extremists in the operation, the spokesman said: "We have mutual interests in going forward in the peace process. We have responsibilities. Accusing an Israeli extremist is not useful."
Palestinian leader Mahmud Abbas did not name any particular group but said a "third party" was behind the attack.
Palestinian security sources had said that the bomber, Abd Allah Badran, belonged to Islamic Jihad, but the group itself has not claimed responsibility.