Basim Salim, 40, who has fled Iraq with his three daughters, told Sweden's Aftonbladet newspaper that conditions at the Malmömässan conference hall had become "completely inhuman".
“Please help us here. We have been here for three nights and can not take any more,” he said. “Some people have been here for five nights. This is not a good place for children, it really isn't. Everyone here is angry and wants to get out. It is like a prison."
A policeman from Stockholm sent to help keep order at the hall wrote on Facebook that he himself had had trouble breathing inside the centre, where nearly 1,000 refugees have been crammed over the past two weeks.
“It stings and itches in your eyes and nose,” the policeman wrote on Facebook, according to Expressen newspaper. “The health services have withdrawn the two nurses they had there because it is not a suitable workplace.”
The policeman wrote that children, many of them with high fevers, were forced to sleep on pieces of cardboard deposited on the concrete floors.
“All those poor children. I was stepping over children's legs and arms, all sticking out under the sheets where they lay cheek by jowl in a row, sleeping on bits of cardboard laid out on the concrete floors,” he wrote.
“Happy children, sad children, children with 40C fevers who are getting neither food nor medicine.”
He said that the 900 to 1000 people estimated to be staying at the centre had to share just six toilets between them.
Rebecca Bichis from Migrationsverket later told Expressen that the nurses had returned, but were now operating from a mobile home parked outside the hall.
The toilets were being cleaned “constantly” from early morning until 9pm, she added.
“Now we are moving the operation to another part of the exhibition halls where there are two to three times as many toilets, and then we can clean the part we used previously,” she said. “If necessary, we can then alternate between the spaces.”
She explained that refugees only spent an average of 16 hours in the hall before being moved on.
Some 190,000 people are expected to seek asylum in Sweden by the end of the year.