One fatality has been reported, Channel 13 in Houston said, from storms that have caused nearly 900 water rescues in the country's fourth-largest city.
The National Weather Service also issued a flash flood watch extending through much of central Texas, into western Louisiana and Arkansas.
Ed Emmett, the top political official for Harris County, signed a disaster declaration for the county that contains Houston after more than 1,000 homes flooded there.
In Houston, more than 70 residential subdivisions reported flooding and Mayor Sylvester Turner canceled his State of the City speech planned for Monday, instructing all non-essential city employees to stay home.
The city has turned one shopping mall into an evacuation center. More than 70,000 customers were without power in the Houston area on Monday morning. As of 12:30 p.m. CDT (1545 GMT), more than 800 flights at major airports in Texas were canceled, according to tracking service FlightAware.com.
In the city of La Grange, near the Colorado River in Southeastern Texas an elderly woman had to be rescued from her truck after it got stuck on a flooded road off of Highway 71.
There were no significant impacts reported for oil fields in Texas and the belt of refineries around Galveston Bay.
Gulf Coast cash refined products markets shrugged off the storm, with spot gasoline prices largely flat with Friday's values.
The rains were expected to cause rivers to crest later in the week, bringing floods to downstream areas, the weather service said.
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