The storm had yesterday damaged a gas line on the platform in the deep water Guneshli section of the Azeri-Chiraq-Guneshli offshore oil field, causing the fire, state energy firm SOCAR said in a statement.
Spectacular footage on Azeri television showed the platform engulfed in flames in the midst of a raging sea.
"Despite bad weather conditions, 32 people could be saved," Aliyev said. "According to preliminary information, one person died. At this time, rescue operations continue."
A mainly Muslim country of nine million wedged between Russia and Iran, Azerbaijan is a key partner in projects to deliver Caspian Sea energy reserves to the West through pipelines to Turkey, bypassing Russia.