Abdul Aziz al-Dueik, the Palestinian legislative council speaker, and 18 Hamas officials appeared before the military court in Ofer, near the political capital of Ramallah in the occupied West Bank on Thursday.
While the defence argued that the defendants deserved diplomatic immunity as they were democratically elected by the Palestinian people, prosecutors insisted the 19 should be treated as members of a terrorist group.
The defence team asked the court for an eight-day extension of the trial to enable them to prepare their argument.
The court then adjourned till September 12 to give both parties time to complete their submissions.
Israeli occupation forces arrested al-Dweik at his home in the occupied West Bank on August 5.
He is the most senior Hamas leader to be charged so far by Israeli authorities, who have arrested about 30 Hamas MPs, including five cabinet ministers since Palestinian armed groups abducted Gilad Shalit, an Israeli soldier, in late June.
Al-Dweik, was later charged with belonging to an outlawed organisation.