Mohammed Nassar, who was an aide to Mabhouh, spoke to Hamas' al-Aqsa radio in Gaza from Damascus. A transcript was released Tuesday.
Israel is widely suspected of being involved in the assassination, but has neither confirmed nor denied the allegations. Israel considers Mabhouh to be responsible for smuggling weapons from Iran to the Gaza Strip.
Nassar says Mabhouh "never stopped thinking about how to fight the occupation by supplying quality weapons to the Palestinian fighters."
The aide also describes how Mabhouh celebrated killing two Israeli soldiers in the mid-1980s by standing on one of the corpses.
Meanwhile, Dubai's Chief of Police Lt. Gen. Dhahi Khalfan Tamim said he has submitted an official request to the UAE Ministry of Justice to arrest Israel's Prime Minister Benjamin Netanyahu and Mossad Chief Meir Dagan in relation to the assassination.
Khalfan Tamim said the involvement of Mossad was certain, adding that the decision to submit an international request for the arrest of Netanyahu and Dagan depends on political authorities.
He also said he did not believe Israel's prime minister would be arrested as a result, but emphasized that "whoever gave the order for the assassination is a murderer."