Scenes of people and pets being rescued from the roofs and upper floors of houses revived memories of Hurricane Katrina in 2005, when early estimates vastly understated both the material devastation and the death toll, and recovery efforts lasted years.

The administrator of the Federal Emergency Management Agency, Brock Long, said on Monday that he expected more than 450,000 people to apply for federal assistance.

“We’re going to be here for several years helping you guys recover,” he said. “The state of Texas is about to undergo one of the largest recovery housing missions the nation has ever seen.”

For the time being, efforts are focused on the most basic elements of keeping people alive — plucking stranded survivors from the flood, providing shelter, food and water, and restoring electricity to hundreds of thousands of people who were left without power.

Mr. Long said that FEMA was shipping two million liters of water and two million meals to the region. Other government agencies, charities and corporations were also moving supplies into the region.

In Harris County alone, several thousand people stranded in vehicles and buildings by the water were rescued by law enforcement and firefighters using motorboats and helicopters, and legions of volunteers used their own boats to ferry people to safety. Governor Abbott activated the entire Texas National Guard to aid in rescue and recovery, raising the number of troops involved to 12,000 from 3,000. And he praised Texans for rushing to rescue their neighbors.

Countless abandoned cars and trucks blocked the region’s flooded roadways, raising questions about whether and how their drivers had escaped safely. They sat at odd angles, some showing no more than a few inches peeking above the water, while others sat half-smashed in roadside ditches or alone in muddy fields.

Almost every evacuee had a dramatic story to tell.

Glenda Walton, standing in a damp gray T-shirt among five family members in an evacuation center, could think only of the day’s events. She said she watched as a woman hugging a tree lost her grip, got caught in the churning water, and drowned.

“She went limp, just like that,” Ms. Walton said.

Officials estimated that more than 30,000 people had taken refuge in emergency shelters, including some that had opened in cities far inland, like Dallas, more than 200 miles from Houston. The mayor of Dallas, Mike Rawlings, said the city had been asked to brace for “numbers that could be up in the tens of thousands.”

In San Antonio, sprawling vacant warehouses had been turn into shelters that could hold more than 4,100 evacuees.