Kraehenbuehl said the situation is "nothing short of catastrophic".
The ICRC has said up to 50,000 people are trapped on a small strip of territory in the conflict zone in Sri Lanka's north.
It called on the LTTE to allow civilians to flee the area, and it urged the government to distinguish between military targets and civilians.
"It is imperative that independent humanitarian organisations also be allowed to provide desperately needed services and relief for civilians still trapped in the 'no-fire zone'," Kraehenbuehl said.
Both sides criticised
The US also expressed concern for the condition of Sri Lankan civilians on Wednesday.
Testifying before congress, Hillary Clinton, the US secretary of state, criticised both the Sri Lankan government and the LTTE.
"I think that the Sri Lankan government knows that the entire world is very disappointed, that in its efforts to end what it sees as 25 years of conflict, it is causing such untold suffering," she said.
As for the LTTE, Clinton said: "There seems to be very little openness on the part of the Tamil Tiger leadership to cease their efforts so that we could try to get in and help the people."
Earlier, Sri Lankan refugees escaping the last remaining stronghold of the LTTE described to Al Jazeera the "hellish" conditions they had endured.
Talking to Al Jazeera's David Chater at a reception centre in Pulmudai, which lies just south of the narrow strip of land held by the LTTE, some refugees said that they had been held on a beach and shot as they tried to flee.
"A lot of them are in a very distressed state. They are suffering from heat exhaustion, dehydration and all sorts of illnesses," our correspondent said on Wednesday.
"I've been talking to the Tamils about the conditions they have been in - they described them as 'hellish'."
Hugues Robert, the head of the mission for Medecins Sans Frontieres which is treating the wounded in Sri Lanka, told Al Jazeera on Wednesday that medical teams in Sri Lanka are "reaching the limit".
"What we are seeing inside the hospital is over 400 freshly wounded people coming to us. The cases are that more than three-fourths of them were injured due to a mine blast or bombshell."
The Sri Lankan military says its so-called hostage-rescue operations are continuing.
Brigadier Udaya Nanayakkara, a Sri Lankan military spokesman, told Al Jazeera that the army "rescued" 40,000 civilians from the northern conflict zone on Wednesday alone.
"We are conducting hostage rescue operations, and up til now 100,000 hostages have been rescued by army troops since the 20th of this month," he said.
"They have been evacuated to welfare camps located in one area."
Officials also said Velayutham Dayanithi, the LTTE's former media spokesman, whose nom de guerre is Daya Master, and an interpreter for group's political wing, known only as George, turned themselves over to government forces on Wednesday.
The war zone of about 21sq km has been split into two sections by the army, our correspondent said.
A Tamil website reported on Wednesday that the Sri Lankan military fired cannons towards a coastal area where the ICRC was preparing to take injured civilians away from the conflict zone.
The LTTE defied a government ultimatum that expired at noon (06:30 GMT) on Tuesday to give up or face a "final assault", saying they will not surrender.
The warning forced tens of thousands of civilians to escape from the conflict zone.
Dr Ghana Gunalan, the director of health services at Trincomalee on the northeast coast, told Al Jazeera that the ICRC had transferred most of the injured to a hospital there.
"Most of these [refugees] have been transported under ICRC flags to Trincomalee. Most people have blast injuries, including to their limbs and abdomens," he said.
"[These injuries] must have been cuased by flying objects that have exploded in front of them."
Mahinda Samarasinghe, Sri Lanka's minister for disaster management and human rights, told Al Jazeera that government forces have not used heavy weapons in the conflict zone.
"If we were using heavy weaponry, by now that area would have been
under the control of the army. It is a very small area that we are talking about. We are taking extreme caution," he said.
Many civilians who have fled the conflict zone are being looked after by the army, he said.
"They are being received by the army, initially checked for weapons and after that they are handed over to the government agency who looks after them in the various camps," he said.
"It is not five-star accommodation but we are trying very hard. There are areas for improvement and we are working on them very consciously."
The UN, which estimates that more than 4,500 civilians have been killed in the past three months, has been one of a number of voices calling for a negotiated truce to allow civilians to leave the rebel-held coastal strip.
The Sri Lankan government has barred independent journalists from entering the war zone.
The LTTE has been fighting for a separate homeland in the north for the country's Tamil minority for 26 years.