Security forces carried out simultaneous attacks against Tamil Tiger defences around Kilinochchi and on the Jaffna peninsula using ground troops and helicopter gunships, the defence ministry said.
In a rare statement announcing casualty figures, the ministry said that 25 troops were killed, with another 10 missing and 160 wounded, while an estimated 120 Tigers were killed and 250 wounded.
For their part, the rebel Liberation Tigers of Tamil Eelam (LTTE) said they had repulsed the multi-pronged offensive by government forces, killing 170 soldiers and wounding 420.
The pro-rebel Tamilnet website quoted Tiger official S. Puleedevan as saying that they had killed 130 soldiers outside Kilinochchi while another 40 soldiers were killed on the nearby Jaffna peninsula.
Puleedevan said they had captured the bodies of 18 government troops and would be returning them through the International Red Cross. He did not give details of rebel casualties.
The defence ministry said sporadic fighting continued in the north while troops were consolidating positions they had captured from the Tigers, who have offered stiff resistance to government forces advancing on Kilinochchi, 330 kilometres (210 miles) north of Colombo.
For several months President Mahinda Rajapaksa's government has been predicting the imminent fall of Kilinochchi and the military recently said it was within "kissing distance" of the town.
But heavy rebel resistance and monsoon rains have slowed the army offensive.
Both sides have claimed to be inflicting heavy losses in the recent battles. Independent reporters and aid workers are banned from the north, making it impossible to verify the casualty claims.
In January the Sri Lankan government pulled out of a 2002 Norwegian-brokered truce.