Reto Meister, head of the ICRC's Asia-Pacific operations, said the northern city of around half a million people was "choking".
"When you can't take in oxygen, you know what the consequences are," said Meister, who had just returned from a five-day mission to Sri Lanka.
Jaffna, which lies on a peninsula, has been cut off by a month-old upsurge in the simmering conflict between government troops and Tamil Tiger rebels.
The city's population, which is already stretched because commercial links have been cut, has been swollen with the addition of about 50,000 refugees from neighbouring frontline areas, who are living a precarious existence in schools and temples.
The Tamil Tiger rebels and government forces have not been able to agree to regular supplies to Jaffna, arguing whether aid workers should travel by land or sea.
"We really wish that the two parties could agree on a logistical chain that would allow these inhabitants to live in a humane condition," Meister told