Residents have been told they can start pushing debris on their properties out to the edge of roadways for eventual pickup.
Standing amid bricks and lumber that used to be her mother's home, Renee Frazier waved at Trump's helicopter as it passed overhead during his aerial tour of the destruction.
A cousin who was in the same house as those killed sustained injuries and is now hospitalized, Griffin said.
"It's been a tragic situation, but a lot of good work is being done", he told reporters at the White House.
Michael Boutwell sifts through the debris while helping his stepdaughter retrieve personal items after a tornado destroyed her home in Beauregard, Ala., Tuesday, March 5, 2019. He said it's possible the death toll could continue to rise, but authorities paused search efforts overnight because conditions are too risky in the dark due to massive amounts of debris.
Lee County Coroner Bill Harris said it's unlikely there are any further victims.
She said authorities are organizing a volunteer reception area for those who want to help.
The National Weather Service said one and possibly two tornadoes struck the area, with a powerful EF-4 twister with winds estimated at 170 miles per hour (274 kph) blamed for most of the destruction. Barbour County experienced two tornadoes, one being classified by the National Weather Service (NWS) in Birmingham, Alabama, as an EF1 and the other as an EF2.
The most powerful was an EF4 tornado blamed for killing 23 people in Beauregard, Alabama, as it travelled roughly 70 miles (112 kilometres) on a path that also left a trail of destruction in western Georgia.
Earlier in the week, Trump said he had told the Federal Emergency Management Agency, or FEMA, to give "A Plus" treatment to Alabama in the wake of the tornadoes. The Storm Prediction Center says a vast part of the region from Texas to Georgia will be under threat of severe weather Saturday. It is known as the "Ash Wednesday Storm" and caused more than $200 million (1962 dollars) in property damage and major coastal erosion from North Carolina to Long Island, New York.
Sheriff Jay Jones in Lee County, where the tornado hit ground in the town of Beauregard, said that the number of those unaccounted for had been reduced to a handful.
"At this stage, it does look like hail is the biggest thing to worry about but we can't completely rule out tornadoes".
Just down the road, where several people died, Trump supporter Bobby Spann said he hoped the president learned "how to be a Southerner, and how to respect people" during his brief visit.
The search took its toll around Beauregard, an unincorporated area of about 10,000 people near the Georgia line.
Rescue crews using dogs and drones searched for victims amid splintered lumber and twisted metal Monday after the deadliest United States tornado in almost six years ripped through a rural Alabama community.