Up to 100 may still be trapped inside, police say
The weight of snow on the building, which was housing a pigeon exhibition, was a possible cause, they added.
At least 100 people were injured and up to 100 may still be trapped amid freezing temperatures.
Much of eastern and central Europe is in the grip of a severe cold snap with heavy snowfalls.
Phone calls
A central section of the roof collapsed at 1730 local time (1630GMT), about 90 minutes before the exhibition was to close.
We have 20 dead. Among them, unfortunately, there are probably children
Krzysztof Mejer
regional government spokesman
A second collapse happened about 90 minutes later during rescue operations.
Hundreds of rescuers are working in the dark to try to get to those still inside, as temperatures have dropped to -15C.
Police say trapped people have been telephoning from inside on mobile phones, reporting dead bodies alongside them.
Stunned people, some clutching head wounds, milled around ambulances.
Krzysztof Mejer, spokesman for the governor office in the Silesia region, told private television TVN24 that chidren were among the dead.
I am now very worried about the other buildings here made of similar construction, in particular the shopping centres
Mark Fordham, Katowice
In pictures: Roof collapse
Katowice fire brigade spokesman Jaroslaw Wojtasik said that the situation was changing dramatically.
"Rescuers are reaching people that are trapped and alive, and unfortunately they are also reaching some that are dead," Mr Wojtasik said.
Some of the victims were in serious or critical condition, officials said.
They said several foreigners were among the injured.
Jacob Parade, a journalist with TVN24 in Poland, told the BBC the building was built about six or seven years ago and was about 10,000 sq m in size. The collapse was a huge surprise as the building was so new, he said.
Firefighters are trying to shore up the building
Sascha Kraus told the BBC her father had been at the scene and said there was not a heavy amount of snow on the roof. People were hurt from falling steel beams, her father told her.
Graf Pietro also told the BBC the snow on the roof was not heavy and that those responsible for clearing it had done a good job.
There were more than 120 exhibitors from countries across Europe at the Pigeon 2006 fair.
Polish Prime Minister Kazimierz Marcinkiewicz arrived at the scene, pledging a public inquiry into the accident.
Polish temperatures have fallen as low as minus 35C recently. The death toll because of cold this winter - the worst in decades - had risen to 199 by Friday, Polish police said.
Fifteen people died on 2 January when the roof of an ice rink collapsed under heavy snow in the southern German town of Bad Reichenhall.
In December, at least 14 people, 10 of them children, were killed when a roof collapsed at a swimming pool in the Urals region of Russia. Snowfall was again thought a possible cause.
Contact us with your stories and eyewitness accounts using the form below.
You can send pictures or video to yourpics@bbc.co.uk or by mms by dialling +44 (0)7725 100100.
You should not endanger yourself or others, take any unnecessary risks or infringe any laws.
Name
Your E-mail address
Town & Country
Phone number (optional):
Comments
The BBC may edit your comments and not all emails will be published. Your comments may be published on any BBC media worldwide.
Terms & Conditions
I was in the neighbourhood few minutes after the tragedy and the situation was very bad. Lot of firefighters, police and ambulances. Right now even army help to rescue victims. About one hour ago the prime minister of Poland arrived to the place of tragedy.
Leszek, Katowice Poland
Mémorial pour les victimes de l'effondrement à Katowice.

Le toit d'un centre d'exposition  à Chorzów près de Katowice en Pologne s'est effondré, faisant officiellement 62 morts et plus de 160 blessés, alors que 125 personnes seraient encore sous les décombres.
Katowice, Pologne.
La salle présentait une exposition de pigeons lorsque le toit s'est effondré sous le poids de la neige, selon les pompiers. Plus de 500 personnes auraient été présentes à ce moment-là.
Les secours, aidés par les personnes présentes sur les lieux de l'accident, sont inquiets car les blessés pourraient succomber au froid, les températures étant inférieures à -15°C.