Kuntar, who was jailed in the Hadarim Prison in the Sharon region 29 years ago, after murdering the Haran family members and two police officers during a terror attack on the northern city of Nahariya, made the promise in a letter to Hizbullah Secretary-General Hassan Nasrallah.
The letter was first published in the Palestinian Authority's official daily newspaper al-Hayat al-Jadida and was revealed by the Palestinian Media Watch.
"My dear and respectable master and commander," Kuntar wrote in the letter to Nasrallah. "Peace be with you and with our shahids (martyrs).
"I give you my promise and oath that my only place will be in the fighting front soaked with the sweat of your giving and with the blood of the shahids, the dearest people, and that I will continue your way until we reach a full victory. I send my best wishes and promise of renewed loyalty to you, sir, and to all the Jihad fighters."
Meanwhile Thursday, Kuntar said that Israel and Hizbullah were on the verge of signing an agreement to exchange prisoners that Hizbullah has preconditioned on his release.
Kuntar's statements were made through his attorney, Yaman Zidan, in an interview with the United Arab Emirates-based al-Halij daily. Kuntar said he had the utmost confidence that Nasrallah would invest every effort in securing the release of as many prisoners as possible from Israeli jails.
Zidan added that after Kuntar is set free, "vital information that has never been disclosed will be released." The attorney provided no further details.
Four additional Hizbullah terrorists, who were taken prisoners during the Second Lebanon War, are jailed in Israel and may be released as part of a prisoner swap deal.
Another prisoner, Israeli citizen Nissim Nasser, who immigrated to the Jewish state from Lebanon and was convicted of delivering information to Hizbullah, is expected to be returned to Lebanon on Sunday.
Nasser finished serving his jail sentence last month and has been held in prison since then as a bargaining chip. The State decided to deport him with the help of the Red Cross and the United Nations Interim Force in Lebanon after his lawyer, Attorney Smadar Ben-Natan, threatened to petition the High Court of Justice.
Smadar Peri and Roee Nahmias contributed to this report