Cyerice Martin, right, comforts her sister, Seavia Dixon in Atkins, Arkansas. Photograph: Mike Wintroath/AP
The powerful winds destroyed homes, flattened warehouses and collapsed the roof of a shopping mall.
The victims included 24 people in Tennessee, 13 in Arkansas, seven in Kentucky and four in Alabama.
The severe storms moved eastwards this morning and tornado warnings were posted for Georgia and northern Florida, the New York Times said.
In Arkansas, two parents and their 11-year-old daughter died after their home "took a direct hit" from the storm, the Pope County coroner, Leonard Krout, said.
"Neighbours and friends who were there said: 'There used to be a home there,'" Krout said. Rescuers were carrying out door-to-door searches in an attempt to find more victims.
In Sumner County, Tennessee, a mother was found dead a few metres from where her house once stood. Her baby was found alive a few hundred metres away and taken to a local hospital, CNN reported.
The tornadoes, which also hit Mississippi, were part of a line of storms that raged across the middle of the country at the end of the Super Tuesday primaries, including Tennessee and Arkansas.
As the extent of the damage became clear, candidates including Hillary Clinton, Barack Obama and Mike Huckabee paid tributes to the victims in speeches.
In Jackson, Tennessee, a tornado trapped college students in collapsed buildings.
"It looks like a war zone. Cars and trucks thrown from one side of the campus to the other," Union University president David Dockery told CNN television, which broadcast footage of the college.
Nine students remained in hospital overnight. None had life-threatening injuries, CNN reported.
Elsewhere in the state, a large fire erupted at a natural gas station north-east of Nashville. Authorities said the station might have been damaged by the storms.
In Memphis, high winds brought down the roof of a Sears store. Debris, including bricks and air conditioning units, was scattered on the car park, and around two dozen vehicles were damaged.
In Mississippi, the Desoto County sheriff's department commander, Steve Atkinson, said a tornado had wrecked warehouses in an industrial park in Southaven, just south of Memphis.
"It ripped the warehouses apart. The best way to describe it is it looks like a bomb went off," he added.