Police believe that the men did not have any political or racial motive, and that they conducted the robbery at the behest of a Swedish buyer Anders Hoegstroem.
Mr Hoegstroem, 34, is being held in custody in Sweden, awaiting extradition to Poland.
Mr Hoegstroem founded and led the Swedish neo-Nazi group National Socialist Front in the 1990s, but quit the group and has since spoken out against the extreme right.
Swedish newspapers have reported conflicting interviews with Mr Hoegstroem, one where he apparently confesses to the crime and another where he claims he was the one who tried to stop the theft.
The original sign is in the process of being repaired but Auschwitz museum officials believe it may be too frail to withstand the severe weather conditions of northern Poland.The replica which currently hangs above the gate could be made permanent.