"When I was the Commander I did receive certain complaints of crimes committed by Jayasuriya's brigade mostly to do with crimes perpetrated on those detained during the war," Fonseka told reporters here.
Fonseka was also accused by human rights groups of being involved in war crimes during the final stages of the nearly three-decades-long civil war that ended in 2009.
"I did not put Jayasuriya in-charge of a fighting brigade. His job was to defend the Army's bunker lines and to be in-charge of supplies to fighting brigades in the battle front. I have details of crimes committed by his brigade," the former army chief said.
An international rights group this week had filed war crimes charged against Jayasuriya in Brazil and Columbia.
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He was serving in Brazil as the Sri Lankan Ambassador and returned to Colombo this week at the end of his tenure.
Fonseka, now a government minister, said it was important for Lanka to maintain the good name of its security forces.
"We must investigate crimes committed by a handful of individuals in order to clear the Army of war crimes charges," he said.
Tamil minority and international rights groups claim that Lankan military had killed a large number of civilians and bombed hospital during the civil war.
Sri Lanka had denied committing war crimes in response to consecutive UN Human Rights Council resolutions which sought accountability for rights abuses during the final phase of the conflict.
Fonseka had a fallout with former President Mahinda Rajapaksa, under whom he had served, following which he was charged in a number of cases, ranging from corruption to engaging in politics in uniform.
Fonseka, who was nearly assassinated by a LTTE suicide bomber in 2006, was pardoned by Maithripala Sirisena days after he assumed office as the new president last year.
All ranks and medals denied to Fonseka by the Rajapaksa regime along with his pension were restored.