"Because it took all night for the wounded and sick passengers to disembark we cannot return to collect another 160 patients waiting to be transferred from the war area until Thursday."
The ICRC said at least 16 patients were killed on Monday in shelling of the centre treating wounded civilians in Putumattalan.
"We are shocked that patients are not afforded the protection they are entitled to," ICRC head Paul Castella said. He did not say who was behind the shelling.
The government has strongly denied that it was involved.
"We did not fire at this location on Monday and it is quite possible that the Tamil Tigers attacked them," military spokesman Brig Udaya Nanayakkara told the AFP news agency.
The military in turn accused the rebels of gunning down 19 civilians and wounding another 75 who tried to escape from the dwindling territory they still control.
INSURGENCY TIMELINE
1976: Liberation Tigers of Tamil Eelam form in the north-east
1987: India deploys peace-keepers to Tamil areas but they leave in 1990
1993: President Premadasa killed by Tiger bomb
2001: Attack on airport destroys half Sri Lankan Airlines fleet
2002: Government and rebels agree ceasefire
2005: Mahinda Rajapakse becomes president
2006: Heavy fighting resumes
2009: Army takes main rebel bases of Kilinochchi and Mullaitivu
But that allegation was "categorically denied" in a statement released by the Tigers on the pro-rebel TamilNet website. It said that Sri Lankan army commandos were responsible "in their attempt to forcibly move civilians" away from the conflict areas.
"Sri Lankan military machinery, which has relentlessly killed and maimed thousands of civilians during the past four weeks, is now engaged in a propaganda drive to divert the mounting pressure on the Colombo government by the international community," rebel spokesman C Ilamparithy was quoted by TamilNet as saying.
Because independent journalists are forbidden by the government from travelling to the war zone, it is impossible to verify the claims of either side.
The rebels are now restricted to an area of less than 100 sq km (38 square miles) and analysts say they are close to military defeat.
The ICRC says the recent fighting has claimed hundreds of civilian lives and trapped tens of thousands of people.
The director general of health services Ajith Mendis told the BBC Sinhala service the ministry of health had issued an order for doctors and hospital staff to leave the conflict area to work in government-controlled areas.
The government has rejected international calls for a ceasefire, demanding the rebels lay down their arms.
The Tigers have said they will not do so until they have a "guarantee of living with freedom and dignity and sovereignty".
The rebels started fighting in the 1970s for a separate state for Tamils.
One-Minute World News
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