The storms are part of a large system moving through the southern United States. Cities such as Shreveport, Louisiana, and Jackson, Mississippi, may be affected.
The Robertson County Sheriff's Office said that residents who could not access their homes are being directed to First Baptist Church. Students at Mississippi State University sheltered in basements and hallways as a tornado made its way near the Starkville campus.
The children, ages 3 and 8, perished when a tree toppled onto the back of their family's auto in Lufkin, Angelina County, while it was in motion, the county sheriff's office confirmed.
The large storm system also knocked out power to thousands and caused some flash flooding.
Texas is seeing the beginning of the unsafe and severe storms forecast to slam parts of the Southeast and Ohio River Valley this weekend. Franklin is located about 125 miles (200 kilometers) south of Dallas.
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In Central Texas, Robertson County Sheriff Gerald Yezak told The Associated Press a tornado hit the small city of Franklin, overturning mobile homes and damaging other residences.
A preliminary damage survey found that a tornado with peak intensity of EF-3 and winds up to 140 miles per hour touched down in Robertson County, according to a tweet from the National Weather Service in Forth Worth.
The storm that took two lives in Angelina County was a separate incident from the tornado that pummeled Franklin, Texas, late Saturday morning.However, the cells are part of the same system that developed in West Texas on Friday night and strengthened as it moved eastward through the state. Some people had to be extricated from their homes.
Emergency radio traffic indicated that search crews were having difficulty reaching damaged structures due to downed trees and power lines in the roadway.
Winds of up to 97 km/h were reported in Cherokee County, Texas, damaging two homes in Alto but not injuring anyone. Severe storms crossing a big swath of the South, including parts of Louisiana and MS, have knocked out power to thousands and caused some flash flooding.
The National Weather Service in Memphis, Tennessee said in addition to the fatalities, rescue efforts are underway with entrapments reported. Alto is situated about 140 miles (225 kilometers) north of Houston.