At least 37 deaths were confirmed from Friday's storms, CNN reported. Eighteen people were killed in Kentucky, 14 in Indiana, three in Ohio and one each in Alabama and Georgia.
A tornado watch remained in effect early Saturday in the Florida Panhandle, and damage was reported from possible tornadoes in Georgia and North Carolina.
Maj. Chuck Adams, a spokesman for the sheriff's office in Clark County in Indiana, said the destruction in towns such as Henryville, Marysville, Chelsea and Paynesville made an estimate of the missing impossible.
"Marysville is almost completely gone," he told WHAS-TV in Louisville, Ky.
President Obama spoke Saturday with the governors of Indiana, Kentucky and Ohio to assure them federal aid is available.
Obama expressed his condolences to the families of those who were killed and acknowledged it will take some time to make a full assessment of the damage.
"The administration, through [the Federal Emergency Management Agency], is closely monitoring the storms and their impacts and remains in close contact with emergency officials in impacted states across the country to ensure there are not any unmet needs," the statement said.
Indiana Gov. Mitch Daniels visited Henryville, The Indianapolis Star reported.
"It does appear that people did have warning," Daniels told reporters, saying some high school students survived because of tornado drills. "But sometimes all things that mere mortals can do aren't enough."
Steve Kloepfer of Chelsea told WHAS he decided to drive south to get out of the path of an approaching tornado after watching it on TV. He returned to find his aunt, uncle and their young grandchild were dead, their bodies carried by the storm from their home to a field, and his own house was in ruins.
There were also stories of survival. A 2-year-old girl was found alive in a field in Salem, 20 miles from Henryville, and was reported to be in critical condition in Kosair Children's Hospital in Louisville.
In Kentucky, Gov. Steve Beshear declared a state of emergency Friday.