Hamas has accused Palestinian "collaborators" of working with Israel to commit the murder.
"In Gaza today, the first hearings were held for three (men) accused of killing Mazen Faqha," Assistant Military Attorney General Fadl al-Jadili said in a statement carried by a local news agency.
He named Ashraf Abu Leila as the chief suspect in shooting dead Faqha, a senior Hamas official killed near his home on March 24.
Two other accused men faced a separate session, with Jadili saying they had been tasked by the Israeli security service with tracking Faqha's movements in the period prior to his killing.
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The source added Abu Leila had allegedly been a member of Hamas's military wing, Ezzedine al-Qassam Brigades, for a number of years before being expelled in 2008.
An image allegedly showing Abu Leila's identity card was shared on social media, according to which he was born in 1979 in the Nuseirat refugee camp in central Gaza.
The well-planned assassination in the middle of the Hamas-run Gaza Strip shocked the Islamist movement.
Hamas immediately blamed its arch-enemy Israel, with which it has fought three wars since 2008, and implemented strict border restrictions on those seeking to leave the Palestinian enclave.
Faqha had been in charge of forming cells for Hamas's military wing in the occupied West Bank.
He had spent years in an Israeli jail before being released as part of a 2011 prisoner exchange deal.