The ICRC says there should be an escape route for civilians
The International Committee of the Red Cross (ICRC) says that intense fighting in northern Sri Lanka has caused a "massive displacement" of civilians.
It says thousands of people trapped inside rebel-held territory have had to flee several times in recent months.
An ICRC official, Paul Castella, told the BBC that fighting had stopped relief supplies being delivered to rebel-held areas for nearly a week.
He said that there were serious concerns about a lack of food.
A Sri Lankan military spokesman insisted a supply convoy had been sent to the rebel-held territory and that there were adequate stocks of food.
The ICRC said it was "extremely concerned" no safe escape route had been agreed.
"This has put at risk the lives of patients who cannot receive suitable treatment on the spot and therefore need to be transferred to Vavuniya hospital, in government-controlled territory," the ICRC said in a statement.
The military say that civilians are safer in areas held by them
It said that civilians who had already been forced to move numerous times were increasingly seeking the safety of government-controlled areas.
On Wednesday, the defence ministry said that a total of 1,707 people had crossed over to government-held areas in the first two weeks of January and were given emergency relief supplies.
"Repeated displacements, often involving the loss of their personal belongings, have taken a toll," said Mr Castella.
The ICRC says that thousands of displaced civilians are now concentrated in an area so small that there are "serious concerns for their physical safety and living conditions, in particular in terms of hygiene".
The organisation is one of the few international relief agencies allowed to operate in rebel-held areas.
The government said this week it was fully prepared to handle "the mass exodus of civilians" the fighting with the rebels might cause.
A massive offensive by Sri Lankan troops in recent weeks has left Tamil Tiger rebels surrounded in their last remaining stronghold - the north-eastern coastal town of Mullaitivu.
The Tigers have been fighting for a separate homeland for 25 years. At least 70,000 people have been killed in the insurgency.