The incident took place at Greendykes House, a 15-storey block in the Craigmillar area to the south of the city, with the alarm being raised at 8.58am.
Six appliances were called out, with fire fighters equipped with breathing apparatus dispatched inside the residential building.
Several residents were temporarily evacuated while the fire was brought under control.
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Fire investigators remained at the scene on Saturday afternoon.
The fire, which is believed to have occurred in a flat on the 14th floor, has since been extinguished.
One eyewitness passing the scene told the News: “There was some amount of ambulances with people being removed from the building by fire fighters with breathing apparatus. There were other people waiting at their windows.”
Another eyewitness added: “Last 3 days there has been fires in the building. Yesterday I believe there was two and the people who caused the past ones has been evicted. And I counted 15 emergency vehicles this morning.”
A third agreed: “2nd fire I knew of in 3 days... but now I’ve read there has been a 3rd in that time!”
Greendykes House and its twin tower Wauchope House are the only original housing left in Greendykes, after the neighbouring low-rise blocks were demolished as part of a wider regeneration of the area.