Tuscaloosa Mayor Walter Maddox asked people Thursday to stay off the streets and conserve water, and for gawkers to stay away. He said "sightseers" are only getting in the way of emergency crews.
"This is going to be a very, very long process" of cleaning up and rebuilding, he said. "During this time we ask for patience and we ask for prayers."
Alabama officials have identified isolated cases of looting inside damaged communities, including raids at a crippled manufacturing plant in Marion County and theft of prescription drugs from at least one unattended pharmacy.
In Hackleburg, Ala., northwest of Tuscaloosa, authorities say they have run out of body bags for the dead and are in need of portable showers, tents and flashlights.
Maddox said there has been at least one encouraging sign to emerge from the destruction: community unity.
"What's amazing is when something like this happens, folks forget all their petty differences," he said, standing beside President Obama. "When we're confronted by the awesome power of nature and reminded that all we have is each other."
ABC News Radio, Michael S. James, Mike Marusarz, Jessica Hopper and the Associated Press contributed to this report.