The children, ages 3 and 8, were pronounced dead at the scene, according to Angelina County Sheriff's Department Captain Alton Lenderman.
A tree lies on its side in Franklin, Texas, on Saturday.
Authorities in East Texas say two children were killed after a tree fell on a vehicle as it was being driven during a strong storm.
Details of the MS fatalities, all of which were reported in Monroe County, were not immediately available, WCBI-TV in Columbus, Miss., reported.
On Saturday night, the National Weather Service said the Franklin tornado, which tore up more than half the southern part of the city, was an EF-3 tornado with winds of 140 miles per hour.
The same storm system that dumped rain and pelted hail from San Antonio to Dallas, and through the Houston metro area moved through East Texas and Louisiana.
The National Weather Service Storm Prediction Center is cautioning that, "Strong tornadoes are possible today into tonight from east Texas into MS, with the greatest threat expected between 2PM-8PM CDT".
A curfew was in effect from 8 p.m.to 7 a.m. Sunday in Franklin, Texas, about 125 miles south of Dallas, following a direct hit from a tornado that overturned mobile homes and damaged 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 the National Weather Service in Fort Worth. The Robertson County Sheriff told the AP that two Franklin residents were taken to a hospital with non-life-threatening injuries.
Another possible tornado touched down in the Vicksburg, Miss., area but no injuries were reported Saturday.
Winds of up to 97 km/h were reported in Cherokee County, Texas, damaging two homes in Alto but not injuring anyone.
Meteorologist Monique Sellers said they've received reports of downed trees, as well as damage to buildings and a transmission tower.
Tornadoes embedded in the storms pose a significant risk overnight since they are hard to see and people are less likely to receive warnings while they're asleep, Van Dam said.
The most significant risk of severe weather is expected Saturday, but there's still considerable potential Sunday. Alto is situated about 225 kilometres north of Houston.
Forecasters in central Texas reported a possible twister Saturday in Robertson County, near Hearne and Franklin.
Parts of the state were placed under a tornado watch until 5 a.m. Sunday, the station reported.