The rebel Liberation Tigers of Tamil Eelam (LTTE) sparked the battle and security forces retaliated in kind, the ministry said in a statement.
Continued fighting in the north and east of Sri Lanka in violations by both sides of a 2002 ceasefire has claimed more that 3,000 lives since December.
The fighting has raised fears of a wider conflict after two days of peace talks between the sides failed at the weekend in Geneva.
In Jaffna, an estimated 500,000 people face siege-like conditions as supplies of food and other goods have dropped to a trickle with the closure of the main highway by the government to the south since August.
The Geneva talks, brokered by Norway, aimed to open the road to bring relief.
But both sides accused the other of failure to make concessions.
The government said it was pouring supplies into the peninsula by ship and the postal department Thursday began accepting packages to be delivered to the area by sea.
The conflict is Asia's longest and bloodiest separ