The states of Kentucky, Illinois, Arkansas and Tennessee were badly affected.
Workers were trapped inside an Amazon warehouse in Edwardsville, southern Illinois, after its roof collapsed from storm damage.
Edwardsville police chief Mike Fillback said “at least two” people had died and about 50 were unaccounted for.
He said several people who were in the building were taken by bus to the police station in nearby Pontoon Beach for evaluation.
A wall and part of the roof collapsed, as did the roof above it. At least 100 emergency vehicles went to the scene.
Mr Fillback said rescue crews were sorting through the rubble for survivors and that this process would last several hours. Cranes and mechanical excavators were brought in to move debris.
“Please be patient with us. Our fire personnel are doing everything they can to reunite everyone with their loved ones,” he said on KMOV-TV.
On Friday, Amazon spokesman Richard Rocha wrote: “The safety and well-being of our employees and partners is our top priority right now.
“We’re assessing the situation and will share additional information when it’s available.”
Illinois governor Jay Pritzker tweeted that Illinois State Police and disaster officials were working with officials in Edwardsville and that he was monitoring the situation.
“My prayers are with the people of Edwardsville tonight, and I’ve reached out to the mayor to provide any needed state resources,” he said.
Kentucky has been hit particularly badly, Governor Andy Beshear said on Saturday.
“The death toll from this event will exceed 50 Kentuckians, probably closer to 70 or 100 lost lives. Each of these people are children of God, irreplaceable to their families and to their communities,” he said.
The storms were some of the worst to hit the state in a long time, Mr Beshear said.
President Joe Biden approved an emergency disaster declaration for Kentucky on Saturday and pledged to support the affected states.
“I promise you, whatever is needed — whatever is needed — the federal government is going to find a way to provide it,” Mr Biden said.
At least one death was reported in Missouri.
Dean Flener, spokesman for the Tennessee Emergency Management Agency, said two storm-related deaths had been reported in Lake County, in the state’s northwestern corner.
Another death was reported in neighbouring Obion County, he said. He had earlier reported two deaths in the county.
The National Weather Service office near St Louis reported “radar-confirmed tornadoes” in the Edwardsville area at about the time of the collapse.
Workers at the weather service office took shelter when another torn passed near their office in Weldon Spring, Missouri, about 48 kilometres west of St Louis.
One person died and two others were injured in building collapses near the towns of Defiance and New Melle, each only a few kilometres from the weather service office.
Nursing home devastated
A tornado struck the Monette Manor nursing home in Arkansas on Friday night, killing at least one person and trapping 20 people inside the building when it collapsed, Craighead County judge Marvin Day told The Associated Press.
Within two hours, the building had been evacuated and everyone initially believed to have been inside had been accounted for, he said.
“It looks like it’s pretty much destroyed,” Mr Day said of the building.
“It happens quick but apparently there was a little bit of time with tornado sirens going off.”
Some residents were found in the basement “and were prepared for this,” he said.
Five people had serious injuries, and a few others had minor ones, he said. The nursing home has 86 beds.
Mr Day said another care home, about 32 kilometres away in Truman, was badly damaged but no injuries were reported. The building is unsafe and was evacuated, he said.
One person was flown by helicopter to hospital.
Candle factory destroyed
The storms caused additional damage as they tracked through Tennessee and into Kentucky.
Kentucky Governor Andy Beshear declared a state of emergency on Saturday and said several western counties had been badly damaged.
He said the National Guard had been summoned to respond to the region.
Several buildings collapsed in the southwestern Kentucky community of Mayfield, said Sarah Burgess, a police officer in the town.
She said several people were trapped inside a damaged candle factory in Mayfield and that a shift was under way there when the storm hit.
“The entire building is essentially levelled,” she said.
Although no deaths were immediately reported in the town, coroners were summoned to the community, Ms Burgess said. “We do expect loss of life.”
Photos posted to social media from Mayfield showed uprooted trees, smashed windows and a courthouse steeple sheared.