Haniya also warned Israel that Palestinians "will not abandon their rights to defend themselves and resist the occupation".
In the exclusive interview, Haniya accused Avigdor Lieberman, the new Israeli vice-prime minister, over the recent deaths.
"The government calls on all the Palestinian people to unify in the face of this barbaric attack," he said.
"Lieberman [is responsible for these] strategies of killings and massacres, [of] killing children and women sleeping safely in their houses," he said.
"They want the Palestinian people to abandon their rights of resistance and self-defence.
"I assure all Palestinians that these killers and occupiers will be eliminated."
Haniya's comments came as the Palestinan government announced general national mourning for three days in all Palestinian territories following the deaths in the Gazan town of Beit Hanoun.
Haniya also urged action from the Arab League following the deaths, saying the ongoing Israeli and EU/US blockade of the Palestinian territories was harming the people.
"Why does the Arab League not convene? Why does the Islamic Conference Organisation not convene?" he said.
"The government will co-ordinate efforts with the president to activate regional and international efforts to halt the Israeli massacres and bloodshed"
Ismail Haniya, Palestinian prime minister
"A nation is being slain, a land is being destroyed. Jerusalem, al-Aqsa mosque and Islamic and Christian shrines are being desecrated in the Palestinian lands.
"I call on the Arab Summit to break the blockade imposed on the Palestinian people and allow entry of money, food and medicines to the sons of the Palestinian people who are defending the Palestinian land and the Palestinian, Arab and Islamic dignity.
Haniya also said the Arab League should not continue to comply with the United States, which he said had "given Israel the green light and which considers killing the children, women and elderly people in Beit Hanoun and Jenin as self-defence".
Haniya then read to Al Jazeera a government statement declaring a suspension of talks - as a result of the Israeli massacres - over the formation of a national unity government in order to mobilise all efforts to save the people in Beit Hanoun and Jenin in the West Bank.
"The suspension of talks comes so that all sides can dedicate their efforts to face the Israeli aggression and activate Arab, Islamic, regional and international efforts," Haniya said.
"The government will co-ordinate efforts with the president to activate regional and international efforts to halt the Israeli massacres and bloodshed."