Sheikh Ahmad, with his trademark ponytail hairstyle tied back, declined to comment to The Associated Press after the two-hour hearing.
He denies the charge and his lawyer, Patrick Hunziker, said in court the sheikh had "no fear" of facing the accusations.
Prosecutors say Sheikh Ahmad, al-Haroun and three Geneva-based lawyers arranged a false arbitration case in the city in 2014 to help authenticate video recordings the sheikh had given to Kuwaiti authorities.
The footage appeared to show a former prime minister of Kuwait and a former speaker of its parliament plotting to overthrow the then-Emir of the oil-rich kingdom.
Prosecutors described in their indictment "accusations of corruption and treason in particular which could have led to the death penalty" for the two men.
The former prime minister, Sheikh Nasser al-Sabah, and the family of Jassim al-Kharafi, the former speaker who has since died, filed the criminal complaint in Geneva more than five years ago.
A lawyer for Sheikh Nasser said the trial delay "is no surprise."
"I think it should have been orchestrated between some parties," lawyer Jean-Pierre Jacquemoud told the AP outside court.
Since being indicted in November 2018, Sheikh Ahmad has been "self-suspended" from two prominent Olympic roles. He has been an International Olympic Committee member since 1992 and has been leading the group of national Olympic bodies, known as ANOC, for nine years.
The sheikh has still been active in Asian sports politics while awaiting the criminal trial.
The Olympic Council of Asia, which the sheikh has led for 30 years, announced a deal in December that gave regional rivals Qatar and Saudi Arabia each one edition of the Asian Games. Doha will host in 2030 and Riyadh four years later.
The trial adjournment should extend Sheikh Ahmad's formal IOC exile beyond its presidential election at an online meeting on March 10. Thomas Bach is running unopposed.
The sheikh's lobbying for Bach in 2013 added to his kingmaker reputation.
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