AUSTIN, Texas — A new round of storms dumped more rain on flooded parts of Texas on Thursday, scrambling transportation, further swelling rivers already spilling over their banks and sending more people to evacuation shelters to escape the rising waters.

The National Weather Service issued a flash flood warning for parts of east Texas and Louisiana on Thursday and placed most of Texas on a flash flood watch due to a slow-moving storm system expected to linger through the weekend.

More than 250 flights were canceled in Houston and Dallas as of 3 p.m. Thursday due to heavy rains, according to tracking service FlightAware.com, while major highways in the city have seen delays caused by accidents linked to the storms, transportation officials said.

Texas Gov. Greg Abbott declared a state of disaster in 31 counties on Wednesday, mobilizing state resources to help cope with the disaster.

Six people were killed in the past week in Texas due to severe weather.

Thousands of people have evacuated their homes in low-lying areas, rivers have swelled to levels not seen in more than 100 years, and emergency workers have completed hundreds of high-water rescues.

Evacuations were ordered for parts of two towns in Fort Bend County, about 30 miles southwest of Houston, where the Brazos River has risen to levels not seen for more than a century.

“The homes are essentially submerged at this time,” said Maj. Chad Norvell with the Fort Bend County Sheriff’s Office. “There is probably 6 to 8 feet of water in some neighborhoods that are close to the river.”

The pounding rains led to some dramatic rescues, including one in the San Antonio area of a man described as a Polish immigrant with limited knowledge of English who suddenly found himself and his car washed away by a wall of water.

Crews putting up flood barricades heard the man scream and a helicopter was sent out to look for him, said James Keith, spokesman for the Bexar County Sheriff’s department.

“We were able to locate this man standing on the top of a submerged car, holding onto a tree,” he said, adding the man was safely rescued.