The National Weather Service said there may have been more than a dozen twisters in all, The Dallas Morning News reported. About a dozen non-life-threatening injuries had been tallied, the newspaper said.
The hardest-hit areas appeared to be the communities of Forney, Lancaster and DeSoto, all outside Dallas, the report said.
"This is just unreal," one person in Lancaster, where about 300 homes and businesses were damaged, told WFAA-TV, Dallas. "You see it and you hear about it, but when you're actually in it, it's just unbelievable."
Arlandra Garrett of Lancaster said the tornado that roared by her apartment building was terrifying.
"Everybody started screaming," she told the Morning News. "Then the apartment started shaking, and then we heard a lot of noise. The lights went off.
"It was over real quick. It was over faster than four blinks."
Jazmine Daniel, 24, said she saw a funnel cloud drop from the sky.
"When it hit, it was taking the windows out of the Walgreen's. It sounded like a bomb went off," she said.
"It was like 'The Wizard of Oz,'" Gwen Dabbs of Lancaster told CNN.
Heavy damage was reported at Six Flags Amusement park in Arlington and large hail fell north of Irving, Accuweather.com reported. All planes were grounded at Dallas-Fort Worth Airport, where the Morning News reported more than 110 aircraft were damaged.
The first funnel cloud was reported on the ground in Ellis County just after 1 p.m. and warning sirens were sounded in downtown Dallas, ABC News said. A second twister was reported near Arlington about 2 p.m. and a possible third was spotted near Texas Motor Speedway.
The National Weather Service reported "large and extremely dangerous" twisters south of Dallas and Fort Worth, with the Dallas airport in the path of a strong tornado. Severe damage was reported south of Fort Worth and south of Dallas and there were reports of damage inside the city limits.
A tornado watch remained in effect until 8 p.m. Tuesday night for 33 counties in north-central and northeastern Texas, including Anderson, Henderson, Hopkins, Rains, Van Zandt and Wood counties, the weather service reported.