It is impossible to confirm which side fired the shells as access to the war zone is restricted by the military, but government officials have repeatedly denied shelling the 12km "safe zone".
There has been no comment on the claims from the LTTE.
The Sri Lankan military says that more than 50,000 civilians have escaped the area since January, but accuses the separatists of stopping many more from leaving.
A statement on the government's website said that the latest exodus had seen 1,515 people, including nearly 650 children, cross into military-controlled areas near Puthkkudiyirippu, the last town held by the LTTE, on Tuesday.
Christian Aid, a British-based charity, said on Wednesday that the situation for the civilians was "becoming graver by the day".
Supplies of food, medicine and fresh water are running low and the group urged the two sides to allow greater access to aid workers.
The UN estimates that 2,800 civilians have been killed in the fighting since late January. The Sri Lankan government disputes that figure.
Meanwhile, the military said it had overrun the hideout of the LTTE's intelligence chief Iranapalai on Tuesday.
"The safehouse was used by both Pottu Amman and [his deputy] Kapil Amman, two of the most-wanted terrorists," the ministry said in a statement.
Pottu Amman is wanted, along with Velupillai Prabhakaran, the LTTE leader, by neighbouring India in connection with the 1991 assassination of Rajiv Gandhi, the former prime minister.
It is not clear if either man is still in Sri Lanka.
The military also said on Wednesday it had repulsed an LTTE counterattack in the north of the island, killing at least a dozen separatist fighters.
"Over a dozen LTTE bodies were observed lying left at the battlefront following heavy fighting," the military said in a statement on its website.
The LTTE has been fighting since 1983 for an independent state in the north and east of the island for the Tamil minority, which suffered decades of marginalisation at the hands of governments dominated by the Sinhalese majority.
More than 70,000 people have been killed in the fighting.