Neck wounds are thought to have led to the death of the American woman who was found stabbed to death at the US Naval Base in Keflavík on Sunday night reports Morgunbladid.
Other wounds were found on the body pointing to the fact that there had been a struggle.
It is not known if the murder weapon has been found nor if the the US soldier has admitted to the murder.
The Icelandic woman, who is said to have had a relationship with the suspect underwent questioning on Monday and was questioned again yesterday.
Morgunbladid reports that investigators are trying to understand certain new facts that have been revealed during the course of the investigation. It is thought that the Icelandic woman was at the crime scene or close to the crime scene when the murder took place.
The US soldier had no prior criminal record but was under investigation for embezzling funds among other things. IR reported yesterday that he, in collaboration with another US soldier, stole money off of her credit card.
Five investigators from the US Navy arrived in Iceland from the UK yesterday. They will be in charge of the investigation both questioning and technical details.