He described the damage as "catastrophic", and said he expected the death toll to rise. But Sheriff Jay Jones said the list of missing people had shrunk from dozens to just seven or eight.
He said: "It looks like someone has taken a giant knife and scraped the ground".
Almost 2,000 homes in the affected area are without power following the tornadoes.
Rescue efforts were halted overnight because of the dangers associated with searching in the dark.
"My heart breaks for all the folks across the area impacted by this deadly storm", Rogers said.
The tornadoes there struck at about 14:00 (20:00 GMT) on Sunday, carving a path at least a half a mile wide and at least a mile long.
Footage of the aftermath shows snapped communications poles, roads littered with debris and wrecked houses.
"Typically, in the Southern plains of the U.S.in what they call the traditional tornado alley, that would be a fast forward speed", said Chris Darden, meteorologist in charge of the weather service's Birmingham office. "And it's that old cliché that it sounds like a freight train coming, well that's what it sounded like".
Residents of Smiths Station told local TV they had seen businesses destroyed there.
Tornado warnings were also issued for Georgia, Florida and SC.
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Tornadoes were also reported in Walton County and Cairo in northern Florida. He said he found more than a half-dozen bodies or fatally injured residents along Lee County 39, the road where so numerous family members died.
"Y'all, it's horrendous, absolutely horrendous", Gov. Kay Ivey said after touring some of the worst devastation in an area of Lee County where "nothing's left standing, everything's in shreds".
According to tornado researcher Richard Stokoe at the University of South Wales, elevated death tolls in Alabama can largely be ascribed to the density of mobile homes, housing nearly 15% of the state's population, the geography of the region and type of coniferous vegetation. "To know Alabama, is to know that we are a tightly-knit community of people".
The tornadoes struck eastern Alabama on Sunday, levelling homes and carving a path nearly a kilometre wide in some parts of the state.
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Trump met privately with more victims' families inside the church.
"Convoy of Hope's Disaster Services Team is headed to Lee County where they will meet with local officials and partners to further develop Convoy's response strategy", says Jeff Nene, Convoy of Hope's national spokesperson. Warm air flows north from the Gulf of Mexico at the same time as storm systems are propelled into the south and mid-west by a southward dip in the jet stream.
A broader area that includes more than 10 million people - stretching from east Texas to Alabama, Tennessee and Kentucky - is at a slightly lower risk of severe storms and tornadoes.