Amnesty said the Tigers were holding civilians hostage and were "reported to have deliberately attacked civilians that have tried to escape from areas under their control."
The government estimates some 70,000 people remain inside.
On Thursday John Holmes, the UN's top humanitarian official, estimated that 150,000 to 190,000 civilians were trapped by the fighting and could not escape, resulting in dozens of deaths each day.
Sri Lanka says the LTTE must first lay down its arms before any ceasefire. It has accused the rebels of using such truces in the past to rearm and regain strength. It said the shooting took place as 381 men, women and children fled the war zone on Friday and sought shelter in government-controlled areas.
Sri Lankan troops have boxed the rebels into a tiny strip of jungle along the island's northeastern shoreline.
Since the beginning of January more than 55,000 civilians have escaped Tiger-held areas, according to the military.
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Fighting also rag