The UN said conditions had to be improved at the camps for civilians
The UN and aid agencies have appealed to Sri Lanka to allow them access to injured and displaced civilians stranded despite an end to fighting.
"Total access" was urgently needed to the rebels' final stronghold, a north-east coastal strip, the UN humanitarian office said.
Thousands of civilians, many injured and sick, are believed to be there.
Sri Lanka declared an end to civil war with the Tamil Tiger rebels following the rebel leader's death.
"We need to have access, I repeat, total access, without the least let or hindrance, for the UN, for NGOs (non-governmental organisations) and for the Red Cross," said Elisabeth Byrs, spokeswoman for the UN Office for the Co-ordination of Humanitarian Affairs.
The UN also called on authorities to improve the situation at camps where thousands had arrived to escape the intensive fighting in the past few months.
SRI LANKA CONFLICT TIMELINE
1976 - LTTE formed
1983 - First attacks by Tamil Tiger rebels; start of 'First Eelam War'
Feb 2002 - Government and rebels sign ceasefire
2004 - 2008 - Violence mounts
Jan 2008 - Government pulls out of ceasefire agreement
Jan 2009 - Government captures Tigers' Kilinochchi headquarters
May 2009 - Government declares victory against Tigers
"It's urgent that assistance gets into those camps and that we are able to deliver," said UN refugee agency spokesman Ron Redmond.
"We've got lots of humanitarian supplies that need to be delivered."
He said the government must improve conditions, maintain law and order and alleviate overcrowding at the camps.
He also said public buildings should be allocated for new arrivals while the UN refugee agency prepared land for new camps.
Meanwhile, the International Committee of the Red Cross (ICRC) said its local staff who worked in the conflict zone were still missing.
Apart from the northern Jaffna peninsula, the ICRC has no access north of Omantai.
Omantai is a small town through which thousands of displaced Tamil civilians have poured after escaping from the fighting. There they have been screened by the army to distinguish Tamil Tiger members from civilians.
Paul Castella, head of the ICRC in Sri Lanka, told the BBC there were still civilians north of Omantai and he was pressing the authorities for access, to assess the needs of those who are hungry and thirsty, sick or wounded.
The Red Cross is also concerned that proper funeral rites be carried out for those who have died, and that their families be notified of their fate.
While the fighting was continuing, the ICRC was the only outside agency with access to the area of combat, taking in aid and evacuating wounded people by ship.
On Tuesday pictures of the body of the man who is believed to be rebel leader Velupillai Prabhakaran were released.
The Tigers had been fighting for a separate state for Tamils in the north and east of Sri Lanka since the 1970s.
About 80,000 people have been killed in the conflict and thousands displaced.