"The killers used the drug succinylcholine to sedate (Mahmud) al-Mabhouh before they suffocated him," the statement quoted Major General Khamis Mattar al-Mazeina, deputy commander of Dubai police, as saying.
"The assassins used this method so that it would seem that his death was natural," the statement said, adding that "there were no signs of resistance shown by the victim."
Succinylcholine is used to induce muscle relaxation and is favored by anesthetists and emergency doctors because of its fast onset.
Dubai police chief Dahi Khalfan Tamim said Friday that he possessed the DNA of at least one of the assassins.
"We've (identified) traces of DNA on the scene, belonging to the criminals," he told al-Arabiya satellite TV. "We have fingerprints and DNA traces and we know what they look like (thanks) to cameras that have revealed the whole operation."
Tamim also said he plans to appoint an international investigation team to pursue the 26 people suspected of committing the murder.
He estimated that the Interpol would put 15 of the new suspects on its most wanted list as early as next week. He said a delegation on behalf of the Dubai police had visited a number of European countries as part of the investigation which led to the assassins' exposure.
Mabhouh, one of the founders of Hamas' military wing, was found dead in his hotel room on January 20.
Israeli intelligence service Mossad has widely been accused of carrying out the Cold War-style hit.