More than a foot of rain had fallen by Monday evening in parts of Houston, submerging scores of subdivisions and several major interstate highways, forcing the closure of schools and knocking out power to thousands of residents who were urged to shelter in place.
Four fatalities appeared to be weather related, authorities said.
Sylvester Turner, mayor of the nation's fourth-largest city, told residents to stay home to fend off a weather system he called "stubborn." More rain was projected over the next two to three days, although heavy downpours had subsided and only another half-inch was expected through Monday night, he said.
Rain gauges in parts of Harris County, which includes most of Houston, showed water levels approaching 20 inches since late Sunday night, with slightly smaller amounts elsewhere in Southeast Texas as bayous and creeks overflowed their banks.
Harris County Judge Ed Emmett, the county's chief administrator, said two bodies were found in a vehicle shown on traffic cameras driving around barricades and unsuccessfully attempt to navigate a flooded underpass.
In addition, one person, believed a contractor with the city's airport system, was found in a submerged vehicle not far from the airport. A second person, a truck driver, was found dead in the cab of his rig after encountering high water on a freeway service road.
Several shelters were established for people forced from their homes. At least 1,000 people taken from apartment complexes in the north part of the city and moved to a shopping mall were being ferried by city buses to a shelter, the mayor said.