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More than 40,000 households across five states were still without power Monday morning as a severe thunderstorm system that killed two people Sunday continued to sweep the South.

The Weather Channel reported that customers in Louisiana and Mississippi were most severely affected by the outages, with Alabama, Georgia and Texas also signaling issues with power supply.

On Sunday, a Louisiana woman and her young daughter were killed when the same system moved through that state.

The sheriff's office in St. Martin Parish, Louisiana, confirmed that Francine Gotch, 38, and her daughter, Neville Alexander, 3, were killed when a tornado flipped over their trailer about 9:30 a.m. (10:30 a.m. ET) Sunday in Breaux Bridge, just northeast of Lafayette.

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A tornado watch remains in effect until 0900 CDT Monday for central, southeastern and east central Mississippi, and dozens of schools will also close today across Alabama, along with the University of Mobile.

The National Weather service (NWS) reported flash flooding in Mississippi and Louisiana overnight, with at least two people rescued from floodwaters in Vicksburg, Mississippi. The system is likely to continue to spin off tornadoes, dump large hail and threaten severe flooding well into the new week.

"This is a statewide weather event," Gov. John Bel Edwards said in an address televised statewide. "Moreover, this is likely to be an all-night event. We don't expect this weather event to leave the state of Louisiana until sometime tomorrow midmorning."

The NWS issued a "particularly dangerous situation" tornado watch through Sunday evening over a wide area from east Texas through central and northern Louisiana and into west central Mississippi.

The National Oceanic and Atmospheric Administration's Storm Prediction Center issued a rare "high risk" warning, with the potential for strong and extensive tornadoes, damaging wind and large hail.

The storm system will continue moving east through Monday, forecasters said.

Big severe thunderstorm supercells expected to sweep across Southeast through Thursday, according to #NationalWeather Service @NWSSPC. pic.twitter.com/8mdetUh6Za — Alex Johnson (@MAlexJohnson) April 2, 2017

"We've got a large territory that these storms are going to be moving across," said Danielle Banks, a meteorologist for The Weather Channel. "As we go through the day on Monday, into the heart of the afternoon, those storms are going to be sweeping through states like Georgia and Florida and over into South Carolina and North Carolina."

In Shreveport, Louisiana, firefighters resuscitated a family's dog on Sunday morning when it was found unresponsive after the home caught fire, fire crews said.

Lightning was suspected of having started the fire, Clarence Reese, emergency management officer for the Shreveport Fire Department, told NBC affiliate KTAL.

The dog and the five members of the of the family were doing fine, Reese said, but the home suffered fire, smoke and water damage.