"Lives are being lost because access is being denied to life-saving medicine," the federation president, Astrid Heiberg, said.
The Red Cross said it was unacceptable that anti-Aids drugs - and medicines for diseases such as malaria and tuberculosis - should be beyond the reach of people in most poor nations.
In recent months, some drug companies have responded to the growing criticism by reducing prices.
But a senior Red Cross official told the BBC that the drug companies were taking a "piecemeal" approach to the problem in an effort to stave off the criticism.
Dr Alvaro Bermejo, head of the health department at the International Federation of Red Cross and Red Crescent Societies, said more had to be done, with the support of all the firms involved.
"We are looking for a systems approach that will bring together the international community and pharmaceutical companies to find a viable solution that makes drugs available for people who are dying today in developing countries," he said.
Cheaper alternatives
The Red Cross is calling on its members to support countries like South Africa where a major court case is under way to try to establish affordable treatment.
"Lives are being lost because access is being denied to life-saving medicine," the federation president, Astrid Heiberg, said.
"Pharmaceutical companies can and must find a way round this," she said.
The major drugs companies say they are entitled under world trade rules to recover the research and development costs incurred while developing new drugs.
But a number of companies have moved recently to cut their prices in developing countries.
Last week, the drugs company, Merck, said it would supply drugs at cost price to a number of developing countries.
But critics say the move falls short and pointed to the legal challenge brought against drug companies in South Africa, to enable the government to ignore patent rules and source cheaper alternatives in emergency situations.