About 2,000 people were killed by artillery fire, according to TamilNet, a pro-Tamil website.
"More than 2,000 innocent civilians have been killed in the last 24 hours," the website quoted S Pathmanathan, the LTTE's chief arms smuggler, as saying.
Brad Adams, the Asia director of Human Rights Watch, told Al Jazeera that the government's heavy artillery fire has hit civilians.
"Hospitals are wherever medical personnel can provide assistance to people. They are often makeshift and sitting on the ground," Adams said.
"They provide their co-ordinates to the government so that the government will not hit them. And yet our research shows that there have been 30 attacks that have hit hospitals.
"These are government doctors who are providing the co-ordinates. These are not LTTE cadres."
The military has denied carrying out the attacks.
Brigadier Udaya Nanayakkara, a military spokesman, said: "[There] is no shelling taking place.
"We have not used heavy weapons in the area where the Tamilnet says civilians had been killed."
Shanmugarajah said that some government medical supplies had reached the zone in recent days, but staff and supply shortages meant that the situation was "overwhelming".
The LTTE is believed to be close to defeat in its 26-year battle for a separate homeland in the northeast for the island nation's minority Tamils.
The territory they hold has been reduced to a 5km strip of coastline following military advances this year.
Tens of thousands of civilians have been forced to flee to state-run camps outside the zone in recent weeks.
It is difficult to verify reports on the conflict as the government bans journalists and international organisations from the area.