Nor could they determine how the thieves had removed and transported the bulky metal sign.
Krakow police spokesman, Mariusz Sokolowski, said several dozen officers were involved in the case and were focussing on two main hypotheses: that the sign was stolen either by neo-Nazis or to be sold to a memorabilia collector.
However, they were not ruling the possibility it was stolen as an act of revenge on behalf of former inmates of the camp.
Another police spokesman Dariusz Nowak told Polish television station TVPInfo that investigators had received about 80 leads from the public, but were yet to make a breakthrough.
They had shared details with international police organisations including Interpol and Europol, Nowak said. Poland's domestic intelligence agency was also involved.
The sign, which translates as “Work Shall Set You Free,” stood above the gates the notorious camp where an estimated 1.1 million Jews and other victims of the Nazis were murdered. The camp is now a memorial site and museum.
The sign was dismantled and removed unnoticed on Friday morning.
Security at the memorial came under scrutiny in the past two days, with Polish Culture Minister Bogdan Zdrojewski demanding to know why it had taken several hours before police were informed.
Four guards on duty at the time of the theft had been questioned but this had provided no solid leads, police said.
Museum director Piotr Cywinski admitted the entrance was watched only by an internet camera that did not record images. The picture quality wasn't even very good, he said.
Israeli Prime Minister Benjamin Netanyahu called Polish authorities to express his shock at the theft, according to Polish news agency PAP.