Storms and torrential rains have killed at least eight people in Texas and Oklahoma, with flooding turning Houston streets into rivers.
Scores of flights due to arrive in Houston and Dallas were cancelled and hundreds of others were delayed.
Houston Mayor Annise Parker asked the governor to declare the city a disaster area.
The National Weather Service issued a flash flood warning as thunderstorms moved along the Gulf of Mexico coast toward Florida and residents were advised to stay at home.
At the same time a runway at Dallas Fort Worth International Airport was closed after a sinkhole measuring more than seven metres by seven metres opened up on the airfield.
The airport said that the closure of Runway 18L did not affect flight departure times as the airport has six other runways available for use.
The cause of the sinkhole has not been found.
