Yigal Amir killed Rabin on Nov. 4, 1995 to prevent the handover of land to the Palestinians. He has shown no remorse.
On its Web site, the Amir family said 10 years in prison is sufficient punishment for killing Rabin.
"The security situation in Israel has proven that Yitzhak Rabin committed a crime against his people when he surrendered our lives and safety to our most bitter enemy," the statement said, according to the Yediot Ahronot daily. "An offense committed against a criminal calls for a much lighter punishment than an offense committed against an ordinary citizen."
Israeli legislator Ran Cohen has filed a police complaint against the Amirs, and Israel's attorney general is examining whether charges will be filed.
"I have had enough of that family. It makes me feel sick, and it drives me out of my mind every time I hear about their activities against Israeli society," Cohen told Israel Radio on Saturday.
"This family doesn't understand that Yigal Amir killed a prime minister and that if he doesn't rot in a grave he should rot in jail for the rest of his life," he said.
Rabin's former bodyguard offered this more blunt assessment of Amir to the Yediot: the assassin should have been "shot down on the spot like a dog," said Carmi Gillon, who headed the Shin Bet security service when Amir murdered Rabin.
A memorial for Rabin marking the 10th anniversary of his killing will be held Nov. 12. The gathering was postponed by a week to allow former President Clinton to attend.
Amir, who opposed Rabin's peacemaking efforts with the Palestinians, shot Rabin after a political rally. He was sentenced to life in prison without parole.
"Yigal Amir is alive because of an operational failure," said Gillon, who was abroad at the time of the assassination and resigned afterward.
"Unfortunately, the bodyguards didn't respond as they were taught to do," he said. "They failed by not shooting him on the spot like a dog, like any other despicable terrorist."
Gillon refused to confirm the published remarks.
A poll published in Yediot over the weekend showed that 20 percent of the Israeli public thinks Amir should be pardoned.
Gillon said the results did not surprise him. Because Rabin's security detail did not kill Amir immediately, he has become a poster boy for the radical right wing, encouraging political killings, Gillon said.
"The assessment that the next political assassination is upon us is correct," he said. The radical right wing, he said, is now focusing its hatred on another person, Prime Minister Ariel Sharon, he added.