Emergency crews were called to a flat in Greendykes Road on Tuesday, where two men were pronounced dead.
Two men, aged 65 and 40, have been arrested in connection with the incident with detectives continuing their investigation.
On Wednesday, there was a large police presence at the scene, with parts of Greendykes House cordoned off by detectives and police standing guard at the door.
A Police Scotland spokesman said: “Around 8.25pm on Tuesday 1 November 2022, police attended a report of an incident at a flat in Greendykes Road in Edinburgh.
“Two men were pronounced dead at the scene.
“Two men, aged 65 and 40, have been arrested in connection and inquiries are ongoing.”