He will be charged with murder on Friday.
During his first interview he gave his version of the incident.
“He described what had happened from the beginning to the end. He also gave an explanation for why he killed the woman,” said police spokesman Björn Engström.
However, the police would not reveal what the man had said or his motive for the crime.
According to the police the woman was killed in the couple’s apartment in the south of Stockholm in the small hours of Sunday morning. He chopped up the body but left the parts in the apartment until Tuesday, when he drove to Nykvarn in Sörmland and dumped them in Yngern lake.
The murder was discovered when a local resident spotted an unfamiliar man cutting a hole in the ice and stuffing filled plastic bags into the lake.
The witness noted the registration number on the man’s car, and police traced him easily.
The identity of the murdered woman still had not been confirmed on Tuesday, but all indications were that she was living with the 31 year old.
The couple had two small children who have now been taken into care by the social services.