"More than 50,000 people have come out of that area in the past three days and with that we have rescued all the civilians held as a human shield by the Tigers," he said.
He added that security forces were closing in on a "small patch of jungle" still under rebel control.
The exodus in the past three days was the biggest since 115,000 people managed to get out of the war zone after troops breached a Tiger defence line on April 20.
The latest announcement came as Vijay Nambiar, chief of staff to UN Secretary General Ban Ki-moon, arrived in Sri Lanka to discuss the plight of civilians.
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The United Nations described recent fighting in the last remaining patch of Tiger territory as a "bloodbath," while the International Committee of the Red Cross said the situation was "an unimaginable humanitarian catastrophe."
The Sri Lankan military denies targeting civilians and says any deaths among non-combatants is the work of Tiger rebels.
Nanayakkara said those who escaped from t