The assault, which allegedly took place on the December 22 last year, reportedly took place in a housing facility in the northern German city of Hamburg.
The alleged victim, a 14-year-old girl from Hamburg, was in state custody but escaped from child and youth emergency services and found shelter in the migrant housing centre.
Hamburg police reported that a 21-year-old Egyptian man, identified only as Loai E, pushed the girl into a toilet cubicle in the early hours of the morning.
Police spokesman Ulf Wundrack said: "There, the suspect demanded sexual favours, which the 14-year-old rejected. Then the 21-year-old dragged her into a room and sexually abused her against her will."
The suspect came to Germany in 2011 as a refugee, according to local media.
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His application for asylum was rejected the same year, after which the Hamburg authorities tried to deport him to Egypt, according to the German Foreigners' Authority (GFA).
But repeated attempts to deport the asylum seeker failed because the man had no papers and Egypt did not recognise him as a citizen.
A spokesperson for the GFA said they tried to arrange his deportation with the Egyptian authorities at least once a year, most recently in the summer of 2016.
Loai E has a criminal record, including drug-related and violence offences.
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