Officers from Lothian and Borders Police received reports of the disturbance at Castleview House in the Moredun area of the city at 8.45pm on Tuesday.
When they arrived, they found the body of a man in the common stairs. He had been stabbed to death.
A 41-year-old man who had also been stabbed was taken to Edinburgh Royal Infirmary for treatment but his injuries are not life-threatening.
The murdered man has been named locally as Billy McVie, but police say they are still in the process of formally identifying him.
It is understood that a fight had broken out between the two men shortly before the incident.
Police officers maintained a presence at the block on Craigour Place throughout the night. The 16-storey block houses 91 flats.
Detective Inspector Gary Cunningham, who is leading the investigation, said: "We are following a positive line of inquiry in relation to this incident, however we are not yet in a position to identify the deceased.
"At this time I am appealing to any residents of Castleview House who have information that can assist our inquiries to get in touch with police, if they have not already done so.
"Anyone else who has any information that can assist should also get in touch.”
Anyone with any information should contact Lothian and Borders on 0131 311 3131, or Crimestoppers in confidence and complete anonymity on 0800 555 111.
By Cara Sulieman
Source: STV News
South Edinburgh News >