A few days later, after frantically scouring the Icelandic capital and its surrounding areas for clues, the police found her Doc Martens on a dock at Hafnarfjordur, a sleepy town on the outskirts of Reykjavik known for its annual Viking festival, its local rock ’n’ roll bands and its picturesque lava fields.

After reviewing video from the scene, they noticed something else: a fishing trawler from Greenland, the Polar Nanoq, moored to a nearby dock. Not far from it they spotted a small red car. It was parked there at 6:30 a.m., the surveillance video showed, and it was the same model as the vehicle seen next to Ms. Brjansdottir before she vanished. Tracing the license plate, the police learned that the car had been rented by two men from the trawler.

Image The disappearance of Birna Brjansdottir dominated news bulletins across Iceland and about 775 rescue workers volunteered to search for her. Credit... Reykjavik Metropolitan Police

There was just one problem. The men who were now the prime suspects in Ms. Brjansdottir’s death could be on the ship, but the Polar Nanoq had set off for Greenland days earlier. Fearful that the suspects would get beyond their reach, the Icelandic Coast Guard sent a helicopter with a squad of six special forces officers, known as the Viking Swat Team, to intercept the vessel, a spokesman for the Icelandic Coast Guard, Sveinn Gudmarsson, said.

About 90 minutes later, Mr. Gudmarsson said, the squad — part of the only armed police force in Iceland — rappelled onto the trawler and arrested the two fishermen, who did not resist. He said that the ship was aware “the Vikings” were pursuing them and had already altered course to return to Reykjavik. “The weather was bad and there were eight-meter-high waves,” he said. “The crew cooperated.”

Helgi Gunnlaugsson, a sociology professor at the University of Iceland, said the case had captivated and shocked Icelanders not only because killings were so unusual in Iceland — in 2012 it had the third-lowest murder rate in the world after Liechtenstein and Singapore — but because the suspects were foreigners and the case had seemed such a mystery at first.

Icelanders, for all the lack of violent crime in their homeland, are nevertheless fascinated by it, and crime novelists such as Arnaldur Indridason and Yrsa Sigurdardottir are national treasures. Some Icelanders have drawn parallels between the Brjansdottir case and a popular Icelandic television series called “Trapped,” centering on an unsolved murder mystery in a remote village where residents are cut off by heavy snow. In the series, a mutilated torso is caught in a fishing net and the suspects are thought to reside on a boat.