German railways today admitted the central role its Nazi-era predecessor played in the Holocaust, saying that without the cooperation of the network the systematic murder of millions of people could never have happened.

Launching its first ever touring exhibition about the Holocaust, the state rail company Deutsche Bahn (DB) said the tracks and freight of the Reichsbahn were integral to the Nazis' extermination plan.

"Without the Reichsbahn the industrial murder of millions of people would not have been possible," said DB's in-house historian, Susanne Kill.

Three million Jews and Roma - including around 1.5m children - were gathered from across Germany and Nazi-occupied Europe and transported on Reichsbahn railway tracks in cattle wagons to extermination camps.

The process involved carefully kept timetables, reliable contingents of drivers and precise coordination with the military that always had priority over the tracks.

Prisoners were even charged a fare for the journey, allowing the railways to earn millions of Reichsmarks from the death transports. Adults paid 4 pfennigs per kilometre, children 2 pfennigs, while those under the age of 4 travelled free. Trainloads of 400 or more, which amounted to massive overcrowding, received a 50% discount.

But the exhibition, Special Trains to Death, which has opened on Berlin's Potsdamer Platz and will move to railway stations around the country, has courted considerable controversy.

The head of DB, Hartmut Mehdorn, long resisted the idea of showing it at a working railway station, lest it "put off" commuters from using the trains.

He has also refused to allow a "Train of Memory" full of biographies of child Holocaust victims, which is due to reach Auschwitz concentration camp in May, to use its tracks unless it paid tens of thousands of euros.

Mr Mehdorn argued that the topic was better suited to a museum. But supporters said exhibiting it at a railway station would increase its impact and the numbers of people who saw it.

Today the transport minister, Wolfgang Tiefensee, who pushed for the station option despite resistance from within DB, told the Guardian: "I'm glad that people will be confronted with this topic in a public place on their way to or from work, because the question is still one for everyone, not just the railways to answer - how was it possible that people allowed such crimes to happen?"

Max Ansbacher from Würzburg recalled the fear, hunger and cold he felt when, at the age of 15, he was transported by windowless cattle wagon to Auschwitz in October 1944.

"The journey began in the dark," he said. "The wagon shunted backwards and forwards for ages, adding to our sense of insecurity ... people screamed and children and the sick cried constantly.

"We drank water from melting icicles ... we didn't know what Auschwitz was, we only knew it was where we were going. The farmers in the fields laughed at us when we asked them where it was and symbolically sliced their hands across their throats."

A large amount of documentation has helped historians detail the close cooperation between the Nazi regime and the railways which was necessary for the Holocaust to succeed.

In January 1943, Heinrich Himmler, who was head of the SS, the Nazi elite force, wrote to Albert Ganzenmüller, the secretary of state for transport and the deputy director of the Reichsbahn, pleading for more train stock.

"If I have any hope of quickly dealing with matters, I must have more haulage trains. Help me to get more," he said.

Ganzenmüller was the only member of the railways ever to go on trial for organising the deportations. But on his first day in court in 1973 he suffered a heart attack and was declared medically unfit.

Although he lived for a further 23 years, he never faced a further probe into his role.