Pathologists are examining the body of Birna Brjansdottir, found washed up on a beach on Sunday, a week after she spent a night out with friends.
The case has shocked the tiny Arctic nation of just 330,000. Sparsely populated Greenland is in mourning too.
Iceland has fewer than two murders a year - hardly ever involving strangers.
The woman's disappearance sparked the biggest search and rescue operation in Iceland's history. More than 725 volunteers took part.
Spots of Brjansdottir's blood were found inside a hire car linked to two crewmen from a Greenland trawler, the Polar Nanoq. Icelandic special forces flew out to sea on Sunday to bring it back to port and arrest them.
One of her shoes was found near where their vessel was docked, at Hafnarfjordur, south of the capital Reykjavik.
Police in Iceland are questioning two Greenlandic sailors over the suspected murder of a 20-year-old woman, in a case that has shocked Icelanders.