"Both are carrying out ... war crimes and we should exact the full price not only from the minor squads in the field but also from those who send them."
Hanegbi is a member of the Kadima party, led by Ehud Olmert, the Israeli prime minister.
Taher al-Nono, a spokesman for Ismail Haniyeh, the Gaza-based Hamas political leader, warned the attacks were due to Israeli aggression.
"The threats are part of continuing Israeli terrorism and crimes aimed at achieving political gains," he said, when asked to comment on Hanegbi's remarks.
Monday's suicide attack in Dimona was the first suicide bombing on Israeli soil in just over a year.
The attack was initially claimed by three Palestinian groups, including the Fatah-affiliated al-Aqsa Martyrs Brigades.
But Hamas's armed wing later said it was responsible for the bombing, which killed an Israeli woman, the Reuters news agency reported a Hamas source in the Gaza Strip as saying.
The bomber and another attacker, shot by police before he could detonate his explosives belt, were also killed.
The Hamas source said the two men came from the West Bank town of Hebron.
Despite the suicide attack in Dimona on Monday, Israeli and Palestinian negotiators held talks hours later in a reaffirmation of US-backed efforts to achieve a statehood deal.
In 2004, Israel assassinated Ahmed Yassin and Abdel Aziz al-Rantissi, two senior Hamas leaders in the Gaza Strip, killings that Hanegbi said had a "direct effect on the motivation of the Hamas leadership to continue to carry out suicide attacks".