The defendants being tried in four separate trials "are accused of carrying out premeditated murders in aggravating circumstances, terrorist acts and other especially serious crimes," the court said in a written statement.
Two of the trials are taking place in the towns of Tuytepa and Yangibozor, both about 40 kilometres (25 miles) east of Tashkent, and two in the towns of Gulistan and Yangier, both about 100 kilometres from Tashkent, the statement said.
Security reasons had dictated that the trials should be closed, the supreme court said, underlining that this was in line with Uzbek law.
"Taking into account that the court process will require the movement of large number of victims and witnesses, in order to ensure their safety the above criminal cases will take place in closed proceedings," the statement said.
The latest hearings follow the sentencing last month by the supreme court of 15 men to jail terms from 14 to 20 years over the Andijan violence.
Uzbek authorities have said 187 people were killed in the May 13 violence, blaming it all on the actions of Islamic insurgents.
Witnesses say troops fired on
unarmed civilian protesters
Witnesses however said that Uzbek troops opened fire on unarmed civilians and that hundreds of people died.
Thursday's statement confirmed reports by human rights campaigners that additional closed trials were taking place under strict secrecy.
Two of the trials began about two weeks ago and one trial began last week, the rights campaigners said.