Dr Thurairaja Varatharaja, the district's top health official, told news agency AP that the bodies of at least 30 people killed in the shelling, including five hospital patients, were brought to the mortuary.
He said another 117 people, including 66 women and children, were injured in the attack.
"There are a lot of bodies elsewhere, but they have not collected those bodies," he said, adding that the ongoing shelling was coming from the government-controlled area around the town of Oddusuddan.
Varatharaja said another 37 people were killed in the fighting on Tuesday and Wednesday.
However, Brigadier Udaya Nanayakkara, a spokesman for the Sri Lankan military, denied hitting the makeshift hospital or a civilian village.
"We have demarcated the safety zone and we didn't fire into that area," he said.
It is impossible to verify death tolls or battle accounts as journalists are barred from the conflict zone by both the government and rebel fighters.
Separately, the United Nations in Sri Lanka accused the separatists of violating international armed conflict laws by refusing to allow local UN staff and their families to leave the war zone.
"The Liberation Tigers of Tamil Eelam (LTTE) denial of safe passage is a clear abrogation of their obligations under international humanitarian law," the UN said in a statement published on Thursday.
LTTE officials could not be contacted for a response to the UN statement.
The LTTE is now surrounded by government troops and cornered in an area that measures less than 400sq km in northern Sri Lanka.
Aid agencies say about 230,000 civilians are trapped between the advancing government troops and LTTE fighters.
Emelda Sukumar, a district government agent in the region, said civilians were "unable to escape from the shelling" because "when people occupy particular places, the LTTE sends shells from that area, and then the army also targets the same area.
Sukumar is paid by the government to oversee official functions in the region - including the distribution of humanitarian aid.
However, she is under LTTE protection and the government has said its agents in rebel territory are under duress to give a version of events that puts the LTTE in a favourable light.
Tony Birtley, Al Jazeera's correspondent in the Sri Lankan capital Colombo, said rebel fighters were struggling to hold on to their last stronghold around the town of Mullaittivu as the army appeared to gain ground every day.
"Critics are concerned there's no longer talk of a political solution and that the grievances that caused this terrible conflict ... have not been fully addressed"
Tony Birtley, Al Jazeera correspondent, Colombo
"The Sri Lankan government is proudly saying it will be the first time terrorism has been defeated by force," he said.
The LTTE says it is fighting for a separate state for the minority Tamil population, many of whom complain of discrimination under successive ethnic Sinhalese governments since the island gained its independence from Britain in 1948.
However, there are concerns that the government might step back from its promise to follow-up military action against the Tigers with political reforms.
"Critics are concerned that there's no longer talk of a political solution and that the grievances that caused this terrible conflict more than 20 years ago have still not been fully addressed," Birtley said.