Kuntar was convicted of the brutal 1979 killing of a four-year-old girl and her father in an attack in northern Israel. He first shot the man as his daughter watched, and then killed her by smashing her head with his rifle butt. Another daughter, aged 2, died when her mother covered her mouth to prevent her from crying out and revealing their hiding place.
Kuntar is serving prison terms totaling 542 years, and Peretz's refusal to rule out freeing him in exchange for kidnapped soldiers is in direct opposition to long-held government policy not to free terrorists "with blood on their hands."
Political analyst Chanan Kristal told Voice of Israel Wednesday that Labor party chairman Peretz's days are numbered.
MK Tzachi HaNegbi, chairman of the Knesset Foreign Affairs and Defense Committee and a leader in the Kadima coalition with Labor, said that freeing Kuntar would represent a victory for Hizbullah terrorist leader Hassan Nasrallah.
He wrote in a letter to Prime Minister Ehud Olmert and Defense Minister Peretz, "Freeing the murderer as a direct result of the kidnapping would decidedly crown Nasrallah... and raise a question on the justification of the sacrifice of 159 victims" in the war against Hizbullah.
Labor MK Ami Ayalon, who has said he will challenge the Labor chairman in the next party primaries, publicly called upon him to quit his ministerial post. "There are those in the political echelon who are responsible [for failures in the war], and I think Peretz needs to own up to this responsibility and resign," Ayalon said.
Defense Minister Peretz has seen his popularity drop sharply since the war in Lebanon. He was the only Labor minister who did not back the proposed 2007 budget, abstaining in the Tuesday night vote.
Other Labor Cabinet members argued that the government compromise on raising the minimum wage was satisfactory, and they left Peretz as the lone Labor minister prepared to weaken the Kadima-Labor coalition.