The suits are based on Jayasuriya's role as a commander in the final phase of Sri Lanka's civil war in 2009.
The lawsuits against Jayasuriya allege he oversaw military units that attacked hospitals and killed, disappeared and tortured thousands of people in the final phase of Sri Lanka's civil war in 2009.
But Marapona said that there is no credible evidence against him for alleged war crimes.
Jayasuriya left Brazil last month to return to Sri Lanka after completing his two-year tour of service. Jayasuriya had diplomatic immunity in the countries where he was ambassador, and the groups pursuing the suits had hoped to compel governments to expel him.
President Maithripala Sirisena had earlier said his government won't allow any military personnel to be tried for alleged war crimes.