Schools were closed, roads were flooded and residents were told to evacuate as heavy rain continued to lash the Houston area and other parts of South Texas on Friday, placing thousands of people under flood warnings and leaving many without power.

Flash flood warnings were issued early on Friday for more than 840,000 people in Harris, Liberty and Montgomery Counties. About 15,000 customers were without power in those three counties on Friday, according to PowerOutage.us, which aggregates data from utility companies across the United States.

The prospect of more rain came after a disaster declaration was issued on Thursday in Harris County after the San Jacinto River, on the outskirts of Houston, was swelling. People in neighborhoods near the east fork of the river were ordered to evacuate.

On Friday, Harris County’s top executive, Lina Hidalgo, repeated the mandatory evacuation notice for residents half a mile from the river and to the east, saying they were “extremely vulnerable,” with a few hundred structures at risk of flooding.

“This threat is ongoing and it is going to get worse,” she said at a news conference.

“The situation today is threatening to life safety,” Ms. Hidalgo said, adding, “and so we want to signal how important this is.”

Up to 15 people overnight and 11 people on Thursday had been rescued from flooded vehicles or homes, she said. Mark Sloan, the Harris County homeland security and emergency management coordinator, said at the news conference on Friday that law enforcement officials and emergency workers would be put at risk if people did not evacuate as told.

Several school districts were closed, Ms. Hidalgo said.

The Houston Police Department said that, as rain continued to fall in the city, commuters should drive cautiously and slowly, using their headlights because of reduced visibility. Damaging winds, possible hail and isolated tornadoes were possible, forecasters in the Houston area said.

As thunderstorms unleashed heavy rain, accumulations of up to four inches were set to grow by another half-inch to an inch, forecasters said. There was a risk of excessive rainfall through Saturday morning, stretching from West Texas to the Gulf Coast and into the Tennessee Valley, the National Weather Service said.

In Polk County, emergency management officials warned on Friday that the continued rainfall could cause water levels at the Trinity River to rise.

Judson Jones contributed reporting.