The blaze – which police are now treating as suspicious – started in the stairwell of the block of flats in the Gracemount area of Edinburgh, on Thursday, at about 9:10pm.
No people were hurt but a dog died from smoke inhalation.
Detective Sergeant John Graham said: “The fire broke out on the top-floor landing and spread to threaten properties in the stair.
“Some of the occupants were forced to jump from a first-floor window to safety, while another resident was rescued via ladder by the fire service. We are appealing for information, in particular anyone who noticed any suspicious activity in or around the building.”