The ministry said that 13 government troops had been killed and 40 injured.
Independent verification of the Sri Lankan military and LTTE claims is extremely difficult as journalists and monitors are prevented from reaching the frontline of the conflict.
The latest fighting comes after the military said it had carried out air raids on Tiger positions while government troops resumed efforts to enter Kilinochchi.
"Air force fighter jets made seven successive air strikes targeting LTTE defences and strategic locations in Wanni [of which Kilinochchi is the capital]," the ministry said.
The navy on Saturday destroyed an LTTE boat carrying arms and other supplies off the northeastern coast of the island, the ministry said.
The Sri Lankan government has been saying for months that Kilinochchi is about to fall to its forces.
The military’s push towards the town comes after the government pulled out of a 2002 Norwegian-brokered truce with the LTTE in January.
The LTTE has been fighting since 1972 for a separate state for ethnic minority Tamils in Sri Lanka.