"Preliminary investigations indicate that the crime was committed by a professional criminal gang that was following the victim before he came to the United Arab Emirates, it said in a statement.
"The culprits left a trace behind that points to them and will help in chasing and
Izzat al-Rishq, a Hamas official, said: "I cannot reveal the circumstances. We are working with the authorities in the United Arab Emirates."
Israeli officials have so far offered no comment on the incident.
A brother of al-Mabhouh said he had been killed by electric shock after an electrical appliance was held to his head.
"The first results of a joint investigation by Hamas and the [United Arab] Emirates show he was killed by an electrical appliance that was held to his head," Fayed al-Mabhouh told AFP by telephone.
"Material was sent to a Paris laboratory which confirmed he was killed by electric shock."
Al-Mabhouh, who was born in the Gaza Strip but who had been living in Syria since 1989, was allegedly assassinated a day after he arrived in Dubai.
Al-Mabhouh's body was brought to Damascus, where he was buried on Friday.
Rula Amin, Al Jazeera's correspondent in Lebanon, said: "It seems that Hamas has decided to reveal this incident [Al-Mabhouh's alleged killing] about ten days after it happened - it took place on January 20.
"Why they only decided to talk about it now, we still don't know."
Al-Mabhouh is said to have engineered the capture of two Israeli soldiers during a Palestinian uprising in the 1980s and was imprisoned several times by Israeli forces. Israel razed his home in Gaza.
Hamas has said he was an "important" member of Izz al-Din al-Qassam brigades, Hamas's military wing named after a Syrian religious leader who fought British colonial forces in Palestine in the 1930s.