Worst hit was Moore, south of the city, where neighborhoods were flattened and schools destroyed by winds of up to 320km/h.
About 120 people are being treated in hospitals.
US President Barack Obama has declared a major disaster in Oklahoma.
Hours after the storm struck, the frantic search-and-rescue operation is still going on.
Heavy machinery is being used under floodlights to try and find and free those still trapped under the tons of debris.
The town of Moore was hit by a record breaking storm once before - 14 years ago - when a deadly tornado took a similar path.
More people are already known to have been killed this time around.
Hospitals have been treating the scores of injured - many are still critically ill and the authorities warn that the number of dead is likely to increase.
He also ordered the federal authorities to join in the search and recovery efforts which are continuing throughout the night.
Monday's twister hit Moore, a suburb of about 55,000 people, and remained on the ground for about 45 minutes.
The Oklahoma chief medical examiner's office said at least 20 children were among the 91 dead.
Plaza Towers Elementary school took a direct hit: the storm tore off the building's roof and knocked down walls.