"The ICRC and other humanitarian aid agencies deplore this unacceptable situation, in particular because it is having a severe effect on the thousands of newly arrived displaced people who until very recently had to endure unimaginable hardship merely to survive in the conflict zone in the northeast," she said.
Until then, the Red Cross had delivered water, food, personal hygiene kits, baby-care parcels, emergency household items and kitchen utensils to the camp, known as Menik Farm, in the country's north, which housed more than 130,000 refugees, she said.
At least 280,000 people have been displaced due to recent fighting between the Liberation Tigers of Tamil Eelam (LTTE) and the military.
Many of them have been sent to overcrowded camps in the country's north.
Pressure continues to mount on the Sri Lankan government to open areas that have been off limits to journalists and aid workers, amid reports that thousands of civilians were killed in the crossfire between the army and the LTTE in the final weeks of the war.
ICRC 'at work'
But Mahinda Samarasinghe, the Sri Lankan minister of disaster management and human rights, told Al Jazeera that the Red Cross had been given access.
"[I lived] near Pudukuripu, in a place called Padapalaayam ... Every hour the Sri Lankan army fired 400 to 500 shells. We were forced to live inside the bunkers.
"My elder brother was injured in the shelling and he was taken to the hospital ... To remain alive and avoid all the atrocities I escaped to India.
"I escaped to India by boat, travelling with many unknown people."
Pradeepan, Tamil refugee
"The heads of the ICRC in Sri Lanka came and met me, we had a very fruitful productive discussion and the ICRC did inform me that they are back at work ... inside the camps and doing what they were doing earlier, he said on Thursday.
"Our position is that we welcome anyone who wants to compliment the troops of the government but they have to work within a national framework.
"And as long as they work within that national framework we would facilitate them to the maximum," he said.
The United Nations High Commissioner for Refugees (UNHCR) has also called for more assistance, citing the lack of services available for aid workers helping refugees who have left the former conflict zones.
"There are several issues that need urgent attention, including overcrowding and the limited services available at the camps,'' Ron Redmond, the UNHCR spokesman, said.
"Civilians coming out of the conflict zone are sick, hungry and suffering from acute malnourishment and dehydration,'' he said in Geneva.
The Medecins Sans Frontieres (MSF) aid agency said thousands of refugees who had arrived in Vavuniya district are in "desperate need of medical care".
"A staggering 50,000 people have arrived in Vavuniya district since last Friday 16th May. Many thousands more are still expected in the coming days," the aid group said in a statement.
"Despite increasing the number of staff, MSF teams are overwhelmed by the huge and sudden influx of people."
The Coalition to Stop the Use of Child Soldiers has said that it had received verified reports of child abductions from camps in the main resettlement area of Vavuniya, often by paramilitary Tamil groups.
Children as young as 12 are among those taken, the coalition said, suggesting that former fighters - who had allied with the military in the fight against the LTTE - are being used to identify and remove former Tiger child soldiers.
The former fighters have been allowed "unhindered" access to the camps that are guarded by government troops, it said.
The Coalition to Stop the Use of Child Soldiers is an umbrella group of global organisations that includes Amnesty International and Human Rights Watch.
"The motive is slightly unclear," Charu Lata Hogg, a researcher with Human Rights Watch said on Thursday.