The man, who is 37 years old, was arrested on Friday on suspicion of an attempted rape in the west of the Norwegian capital in February.
He was on Monday remanded in custody for four weeks without the right to visits, newspaper Dagbladet reports.
He has now been further placed under suspicion of four additional women in the central and Grünerløkka areas of Oslo, according to the report.
Oslo Police District announced the broadening of the case against the man in a press briefing on Monday.
Police will also investigate his connection with reports of similar incidents.
The four women are reported to have been attacked as they let themselves into their homes after being followed by him.
All are in their twenties and were on their way home from a night out when the incidents occurred, Dagbladet writes.
The suspect has admitted to assaulting the women but has denied attempting to rape them, according to the newspaper’s report.
The attacks took place between December 2017 and the spring of this year.
In court, the suspect said he had strangled the women until they lost consciousness before leaving the scenes of the attacks.
The court did not agree with police that it was overwhelmingly evident that he had attempted to rape the women. He did not appeal against the preliminary detention.
Kari-Janne Lid, head Oslo Police's sex crimes department, told Dagbladet that investigation of attacks on women in central Oslo and Grünerløkka has been ongong for a number of months, with similarities seen between a number of cases.
“We expect charges to be (further) extended,” Lid told Dagbladet, but declined to go into further detail.
The man’s defence lawyer, Sidsel Katralen, declined to comment on the case, but Dagbladet reports he has previous convictions for both rape and assault.