A pro-Tamil website, Tamilnet, said the army fired from all points along the north, west and south of the conflict zone in the early hours of Monday.
The report said about 160,000 civilians were still sheltering in the conflict zone.
"If the expected offensive goes forward, there will be more than 10,000 casualties, as the area is densely populated and there is no cover from bombs, shells, and bullets," the Tamil Rehabilitation Organisation (TRO), was quoted as saying on Monday.
However, a statement from Mahinda Rajapakse, the Sri Lankan president, on Monday, said the government had "decided that combat operations have reached their conclusion".
"Our security forces have been instructed to end the use of heavy calibre guns, combat aircraft and aerial weapons which could cause civilian casualties."
The Sri Lankan government had previously said that no heavy weapons were being used in populated areas and that the operation was merely a "rescue" exercise.
The defence ministry said at least 12 LTTE fighters had been killed and 27 wounded on Sunday.
It said 52 Tamil Tigers, including 29 child soldiers, surrendered over the weekend.
The Sri Lankan air force denied LTTE claims that it had dropped bombs close to civilians, after a Tamil television channel in Canada released a video on Sunday appearing to show a Sri Lankan warplane shelling civilian areas.
Janka Nayakkara, a Sri Lankan air force spokesman, told Al Jazeera: "These are just baseless allegations ... the air force has not carried out any offensive operations."
It is impossible to independently verify the veracity of the video footage as journalists and aid agencies are banned from entering the conflict zone.
Reports of renewed fighting came as John Holmes, the UN humanitarian chief, was visiting the island with a plea to both the administration and the Tamil Tigers to spare trapped civilians.
About 110,000 civilians escaped from the LTTE-held territory last week following an ultimatum by the government for the Tamil Tigers to surrender.
|Holmes, right, is visiting camps for the more than 100,000 displaced people [AFP]
The United Nations estimates that up to 50,000 non-combatants are still in the conflict zone, while the government maintains that the number is less than 20,000.
A UN document circulated among diplomats in Colombo, the capital, last week said as many as 6,500 civilians may have been killed and another 14,000 wounded so far this year.
Holmes met Rohitha Bogollagama, Sri Lanka's foreign minister, before visiting camps in northern Vavuniya where more than 113,000 civilians have sought refuge in camps that are overcrowded and still without enough supplies.
Sri Lanka's government believes that it is on the verge of defeating the LTTE after 37 years of conflict, and has consistently brushed off international calls for a truce.
Gotabhaya Rajapakse, Sri Lanka's defence secretary on Sunday, dismissed the Tiger's truce offer as "a joke".
"What is the need for a ceasefire when they are running away? They should first lay down arms, surrender and let the people go," he said.
"They were not fighting with us, they were running from us. There is no need of a ceasefire. They must surrender. That is it."