Some of the worst clashes were reported in the northern peninsula of Jaffna, where the army and Tamil Tiger rebels exchanged intense artillery fire on Saturday.
Jaffna, which the government holds, is cut off from the rest of the country by rebel-held territory.
The Tigers claimed they had destroyed army checkpoints and were advancing, but the military said it still controlled the whole peninsula.
Sri Lankan officials also said the rebels attacked a key naval base in northeastern Sri Lanka in a push to retake Jaffna.
Both sides are accusing each other of starting the fighting in Jaffna. It comes in the wake of intense skirmishes in recent weeks over a disputed irrigation canal.
Fighting also was reported in the eastern district of Trincomalee. The army says the rebels pounded the area with artillery fire. The rebels accuse the government of launching waves of air attacks in the area.
Truce monitors say hundreds of civilians in Jaffna and Trincomalee are on the run.
The fighting is the worst since the government and the rebels signed a cease-fire in 2002 in an effort to end two decades of civil war.
The deputy head of Colombo's Center for Policy Alternatives, Rohan Edresinghe, says most people, including officials from countries that brokered the truce, expect the situation to deteriorate in the coming days.
"I think it is virtual war for the moment," he said. "The international community, which does exert a lot of influence in Sri Lanka, seems to be a little despondent, frustrated with both sides, wondering what they can do. It is almost as if they too have accepted the inevitability of a limited period of conflict."
More than 400 people have been killed since the fighting broke out two weeks ago.
However, neither side has formally abandoned the 2002 truce.
The Tamil Tigers began fighting for independence for Tamil-dominated areas in the north and east of the country in 1983, after accusing the Sinhalese majority of discriminating against the Tamil community.