Thousands of civilians have been fleeing the conflict zone
Visiting top UN humanitarian official John Holmes has urged Sri Lanka's army and the Tamil Tigers to do everything possible to avoid civilian casualties.
Mr Holmes said both sides should let civilians leave the war zone.
Meanwhile a senior Tamil Tiger rebel has appealed to the international community to create a "congenial environment" for a ceasefire.
The government says the Tigers are using human shields, but the rebels say civilians are seeking their protection.
Tens of thousands are believed to be trapped in the north-east conflict zone.
A key issue on Mr Holmes's agenda is the plight of about 30,000 civilians who have already fled to government-run camps - and the tens of thousands more who may try to join them.
A foreign ministry official told Agence France-Presse news agency that Mr Holmes was expected to travel to the camps in the north-east.
Mr Holmes said: "We are concerned about reports of heavy casualties to the civilian population.
"I call on the government and I call on [the Tamil Tigers] to do everything possible to avoid such casualties and to make sure international humanitarian law is being fully respected."
He added: "I hope to hear no more of shootings of people trying to leave or recruitment of children as soldiers."
This is Mr Holmes's first visit since 2007 when his comment that Sri Lanka was one of the most dangerous places in the world for aid workers sparked government anger and drew a rebuke from the prime minister.
Meanwhile the rebels' political spokesman, Balasingham Nadesan, told the BBC Sinhala service that the rebels were prepared to adhere to a ceasefire immediately if the international community could create a "congenial environment".
Mr Nadesan denied government and UN claims that the rebels were shooting civilians who were trying to flee Tiger-held areas.
"This is malicious propaganda," he said. "There are 300,000 people who want to stay with us because they are confident that we are their guardians."
He also denied UN claims that the rebels were recruiting under-aged soldiers and insisted that although the Tigers are currently surrounded by the army, they have "the confidence and the support of Tamil people to come back".
On Thursday the UN also issued an appeal for $155m in international aid for communities in northern and eastern Sri Lanka hit by the war.
The UN and aid groups have expressed deep concern that there is not enough food and medicine reaching the civilians. They say that a minimum of 2,500 tonnes of food a month are needed.
On Wednesday India offered to help evacuate the trapped civilians.
Sri Lankan defence spokesman Keheliya Rambukwella welcomed the offer, "provided it is done within the framework the we have set up already".
However on Thursday, the government again stressed its opposition to the UK's appointment of Des Browne as a special envoy.
It has called the appointment a "disrespectful intrusion" made without prior consultation.
About 50,000 soldiers are pressing the Tamil Tigers into a patch of north-eastern jungle after taking the key areas of Kilinochchi, Elephant Pass and Mullaitivu.
The Tigers have been fighting for a separate homeland in the north and east for a quarter of a century.