A tornado watch remains valid until 10 p.m. CDT Tuesday evening in 25 counties across North Central Texas, including Dallas, the National Weather Service reported.
Showers and thunderstorms are likely before 1 a.m. Some of those storms could be severe.
The storm should give way to mostly sunny conditions by Wednesday.
A tornado warning remains in effect until 9:45 p,.m. CDT for Dallas County and also for Rockwall, Northwestern and Kaufman counties.
Large damaging hail up to baseball size is also possible. The severe thunderstorm in those areas has a history of producing one or more tornadoes capable of producing an additional tornado near University Park.
Preparations can include moving to an interior bathroom, a close or hallway on the lowest floor of the building. People are urged to cover themselves with blankets, pillows or a mattress for protection.
Some witnesses are reporting that twisters have already touched down in some places, accompanied by golf-ball size hail.
There are confirmed reports in the eastern town of Azle and also extensive damage in Saginaw.
The concern, however, is that the storm moves its way eastward and hits the heavily populated city of Dallas and the Fort Worth International airport.
The twister worries follow one that just wreaked havoc on the city of Joplin, Missouri, killing 117 people -- one of the deadliest on record.
More deaths have resulted from outbreaks of multiple tornadoes so far this year.
On April 27, a pack of twisters roared across six Southern states, killing 314 people, more than two-thirds of them in Alabama.
Speaking from London, President Barack Obama said he would travel to Missouri on Sunday to meet with people whose lives have been turned upside down by the twister.
The American people are by your side, Obama said. We're going to stay there until every home is repaired, until every neighborhood is rebuilt, until every business is back on its feet.
Counties under tornado watch until 10 p.m. CDT include: