BEAUREGARD, Ala. — Days after ferocious tornadoes killed almost two dozen people and devastated block after block of eastern Alabama, officials warned Wednesday that the state should brace for the possibility of more trouble this weekend.

“We have another storm system, very powerful, that will begin entering the state” on Saturday, Kevin Laws, a National Weather Service meteorologist, said at a news conference in the county where 23 people were killed on Sunday. “Most of the entire state’s going to be under a significant risk.”

The Weather Service’s Storm Prediction Center issued a separate forecast that showed much of the South, including Alabama, Arkansas, Florida, Georgia, Louisiana and the Carolinas, in at least some jeopardy over the weekend. Meteorologists, who predicted Sunday’s outbreak with striking precision, are expected to refine their forecast in the coming days.

Mr. Laws said there was a possibility that the eastern half of Alabama, which includes the communities that were hit hardest last weekend, would ultimately face “somewhat more of a minimal risk.”