The UN estimates that about 50,000 civilians are trapped by the conflict, in a three-sq-km strip of land.
A day after Britain and the US called on both the government and the rebels to end hostilities immediately there is no sign of that happening, the BBC's Charles Haviland reports from Colombo.
An ambulance burned outside the hospital in Mullivaikal on Wednesday
Dr T Varatharajah in Mullivaikal told the BBC more than 50 people had died when two shells hit the zone's main hospital compound.
Sources in the UN said they agreed with that figure and that 100 had been injured.
A Sri Lankan technician working for the International Committee of the Red Cross (ICRC), a 31-year-old father, was killed in shelling along with his mother, the organisation said.
There are accounts of dozens more civilians also being killed.
US President Barack Obama's comments on Sri Lanka's crisis
In Washington, President Obama urged the Sri Lankan government to stop indiscriminate shelling, give UN humanitarian teams access to civilians trapped between the warring sides, and allow the Red Cross and other relief workers to help displaced people.
Mr Obama also called on the Tamil Tigers to lay down their arms.
"Without urgent action this humanitarian crisis could turn into a catastrophe," he said.
Shelling of the same hospital in Mullivaikal on Monday night and Tuesday morning left 49 dead and 86 injured, the doctor told the BBC earlier.
A rebel spokesman said a home for mentally disabled women was also shelled, resulting in the death of 38 people.
He blamed the government side but the Sri Lankan military spokesman, Brig Udaya Nanayakkara, said the rebels were spreading false propaganda.
The army was, he said, using only small arms during its military advance and there was, he added, no facility for handicapped people nearby.
Asked about recent video from Tamil sources, purporting to show the aftermath of hospital bombardments, he said the Tigers were booby-trapping all sorts of facilities and people might be caught in that.
The government says it is in the final stages of wiping out the Tamil Tigers but the rebels have said they will not surrender.
Amnesty International has demanded "immediate and unhindered" access to the war zone for international monitors and humanitarian agencies.
Accusing both sides of putting civilians' lives in danger, it urged the UN Security Council to create a commission to investigate "serious violations by all parties in recent months".
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