"We are looking into other suspicions of rape in another incident," said a spokesperson for the public prosecutor's office in response to media reports.
German daily Die Welt reported Thursday that the man had met a young Afghan woman online, who he drugged and raped with an accomplice in Hamburg. He allegedly gloated about the incident online.
The man admitted to police that he killed his sister last week because she had turned away from her family, DDP reported. The family immigrated to Germany from Afghanistan 13 years ago, German news magazine Der Spiegel reported in its online edition. Both siblings have German citizenship.
The girl died early on Friday morning of multiple stab wounds in Hamburg's Sankt Georg district.
The man had already been prosecuted for assaulting his sister and others. He was sentenced in March on an assault charge to one year and five months without possibility of probation, the Hamburg prosecutor's office told German press agency DDP on Monday.
The man had requested his March sentence be deferred, prosecutors said. He was notified in writing on Wednesday - a day before the stabbing - that the request had been rejected.
Police were also investigating earlier claims that he assaulted two of his sisters, including the girl stabbed last week.
A series of six honour killings in Berlin - including the shooting at a bus stop of 23-year-old Turkish woman Hatun Sürücü - shook Germany in 2005. Sürücü's youngest brother, Ayhan Sürücü, later confessed to killing her because he did not approve of her Western lifestyle.