Iceland has been gripped by a rare murder case after a young woman’s body was found on a beach.

The parents of 20-year-old Birna Brjánsdóttir contacted the police on the morning of Sunday 15 January when their daughter hadn't arrived home from a night out. She was last seen leaving a music venue called Hurra in the Icelandic capital Reykjavik at 4am that morning.

Security cameras showed Ms Brjansdottir walking up Laugavegur, the main shopping street in Reykjavik at around 5am and buying a kebab. Her mobile phone was later traced to Flatahraun in Hafnarfjorður, a town just south of the capital.

The complexity of the mission led officials to launch a missing person search with more man power and equipment than ever before in Iceland, a country with one of the lowest murder rates in the world.

The mission, classed Iceland's most high-powered missing persons mission in history, required 57 super jeeps, 17 buses, 12 quadbikes, 15 drones, 11 dogs, four boats and two helicopters (Icelandic Association for Search and Rescue)

Eight days later, on Sunday, the young woman’s body was found on a beach.

Police said in a statement on Sunday they were treating the case as murder, but added that it was “currently not possible to determine the cause of death”. Two Greenlandic sailors aged 25 and 30 were being held in connection with her disappearance.

The week-long search mission saw nearly 600 volunteers from Iceland's largest search and rescue team on the case to find the young woman.

Þorsteinn G Gunnarsson, spokesman for the Icelandic Association for Search and Rescue, which led the search, told The Independent: “It’s very unique for a young woman to disappear in the middle of Reykjavik. It's very unusual. People do not just disappear here."

The week-long search mission saw nearly 600 members of Iceland's largest search and search team on the case to find the young woman (Icelandic Association for Search and Rescue)

The search mission, which started late on Sunday 15 January, began with a sniffer dog identifying a trail of the woman from the nightclub she had left. It led the team from the club up to Laugavegur, the main shopping street — then it vanished.

“The police identified that her mobile had been switched off in Hallgrimskirkja [the country's largest church] on Sunday morning. We had about 130 members of our search team there at this point," said Mr Gunnarsson.

Ms Brjansdottir's shoes — a pair of Doctor Martins — were found in the port of Hallgrimskirkja two days later. A member of the public had come across them and posted a photograph on Facebook in an appeal to find the owner. Police were quick to examine the footwear, and they were soon identified as those of the missing woman.

Surveillance cameras showed a small red car, a Kia Rio, parked near to where the shoes were found at around 6.30am the morning Ms Brjansdottir went missing – identical to a vehicle observed near the spot where she was last seen.

Traces of Brjansdottir’s blood were later said to be found in the red car that had been rented by the sailors.

A call-out was then made to search and rescue volunteers across the country to carry out a major search across the region. At one stage, 750 volunteer members of the search team were searching the possible routes where the woman's potential abductor could have gone.

Ms Brjansdottir was found by Selvogsviti Lighthouse, around 65 kilometres from where she went missing (Google Maps/screen grab)

"It was very difficult land because it was a lot of rough land. We searched 100 metres on both sides of every road," said Mr Gunnarsson.

"On Saturday, we saw the most man-power of any missing person search Iceland has ever seen, with 750 volunteer rescue workers out."

"We have calculated that our people searched 7,000 kilometres of rough landscape in two days in. They found a lot of things, including six smartphones, but nothing that was connected to the case."

But on Sunday afternoon, a week after the search began, one of the team's helicopters identified a body on a beach in Strandarkirkja, by the Selvogsviti lighthouse.

The two sailors arrested in connection with the murder had set sail on a Greenlandic trawler, the Polar Nanoq, a few hours after Ms Brjansdottir went missing.

Members of Iceland’s elite police force flew out to the ship by helicopter to question the crew, and the ship returned to Reykjavik and two sailors were taken into custody. The investigation is ongoing.

Iceland, a country of 330,000 people, has one of the world’s lowest crime rates, with a registered average of 1.8 murders per year since 2001.

With just two recorded murders in the past three years, the tragedy has instilled a sense of shock and grief across the nation.