By Jon Herskovitz
Governor Robert Bentley said in a message on Twitter the four fatalities occurred in a building in the area of Rehobeth, in southeast Alabama just outside the city of Dothan.
The federal Storm Prediction Center listed the incident on its website as a possible tornado. Dothan-based television station WTVY said in a report citing local officials the four people were killed inside a home that was struck by a falling tree and power lines.
Emergency officials in the area declined to comment immediately.
Strong winds snapped power lines in several U.S. states along the Gulf of Mexico coast on Monday, with tornadoes reportedly touching down in Mississippi.
The National Weather Service (NWS) issued tornado watches stretching from Louisiana to Florida and flash flood watches for several states in that area.
"All severe hazards will be possible including damaging winds and tornadoes, especially across portions of southeast Louisiana and central and southern Mississippi through southern Alabama and the western Florida Panhandle," the NWS said.
There were reports of tornadoes touching down in three places in Mississippi, the service said.
"There has been no widespread damage," said Ray Coleman, a spokesman for the Mississippi Emergency Management Agency, which said there were nearly 20,000 customers without electricity in the state due to the storm system.
High winds also knocked down power lines and trees in Texas, including in the Houston area, as well as in Louisiana, the NWS said. Hail fell in several states, including Alabama and Arkansas, it said.
More than 11,000 customers were without power on Monday evening in Texas and Louisiana because of the storm, utility companies reported.
The storms had limited impact on air travel, with 32 flights canceled at Houston Bush Intercontinental Airport, one of the country's busiest, by 6 p.m. (midnight GMT), according to tracking firm flightaware.com.