The state's Office of the Chief Medical Examiner said only one of the victims, a child, was still unidentified. It provided the names for the others in the toll, up from 18 on Monday.
Most of the victims were men. The youngest was Rey Chicoj Pol, a 17-day-old baby swept away with his mother, Maria Pol Martin, 26.
Dorenia Hamilton, 79, was the oldest victim, along with two men in their 60s.
The victims included storm chasers Tim Samaras, his son Paul and their partner Carl Young, who were caught in a twister that struck El Reno, west of Oklahoma City, one of several that hit a region still reeling from a huge tornado that claimed two dozen lives last month.
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They were said to be the first storm researchers ever to lose their lives while pursuing twisters.
The United States is hit by an average of 1,200 tornadoes each year. They are particularly common in the Great Plains states of Kansas, Oklahoma and Texas.