HOUSTON — Tropical Storm Harvey, which tore across the Gulf Coast of Texas as a hurricane, pounded the region with rains measured in feet, not inches, causing catastrophic flooding Sunday.
At least five deaths and more than a dozen injuries had been reported in the aftermath of the storm.
Across the nation’s fourth-largest city and suburbs many miles away, Harvey left families scrambling to get out of their fast-flooding homes. Rescuers — in many cases neighbors helping neighbors — in fishing boats, huge dump trucks, and even front-end loaders battled driving rains to move people to shelter. Some used inflatable toys to ferry their families out of inundated neighborhoods, wading through chest-deep water while the region was under near-constant tornado watches and warnings.
In scenes echoing the turmoil of Katrina in New Orleans in 2005, Coast Guard helicopters plucked residents from rooftops as the waters swallowed their homes.
Emergency officials said they could not keep up with the calls for help. Rescuers had to give top priority to life-and-death situations, leaving many affected families to fend for themselves. Several Houston-area hospitals were evacuated due to the rising waters.
Amid such devastation and despair, the National Weather Service offered an ominous forecast: Before the storm that arrived Friday as a Category 4 hurricane is gone, some parts of Houston and its suburbs could get as much as 50 inches of rain. That would be the highest amount ever recorded in Texas and match what Houston averages in a year.
Some areas had already received about half that amount. Since Thursday, South Houston has recorded nearly 25 inches, and the suburbs of Santa Fe and Dayton got 27 inches.
The director of the Federal Emergency Management Agency, Brock Long, predicted that the aftermath of the storm would require FEMA’s involvement for years.
‘‘This disaster’s going to be a landmark event,’’ Long said.
Federal disaster declarations indicated the storm had so far affected about a quarter of the Texas population, or 6.8 million people in 18 counties.
Governor Greg Abbott said Sunday that 12 counties were added to an earlier federal disaster list of six. He said that President Trump approved the increase.
About 3,000 state and National Guard members had been activated to assist local emergency responders.
About 5,000 federal workers have already been deployed in Houston, including employees of the Federal Emergency Management Agency and the Coast Guard.
Houston officials said they had responded to more than 2,500 emergency calls by Sunday, including 1,000 high-water rescues.
In a rescue effort that recalled the turmoil of Hurricane Katrina, helicopters landed near flooded freeways to pick up stranded drivers in the city, airboats cruised across submerged neighborhoods, and high-wheel trucks plowed through flooded intersections. Some people used kayaks or canoes to flee, or swam.
Thousands of rescue missions were going on across a large swath of Texas, and Abbott said Sunday that more than 3,000 national and state guard troops have been deployed to assist with relief efforts. The Federal Emergency Management Agency said federal agencies have more than 5,000 employees working in Texas, and the White House said President Trump plans to visit areas on Tuesday.
Officials said Houston, a major center for the nation’s energy industry, had suffered billions of dollars in damage.
The flooding was so widespread that authorities had trouble pinpointing the worst areas. They urged people to get on top of their homes to avoid becoming trapped in attics and to wave sheets or towels to draw attention to their location.
‘‘The breadth and intensity of this rainfall is beyond anything experienced before,’’ the Weather Service said. Average rainfall totals will end up around 40 inches for Houston, service meteorologist Patrick Burke said.
On Sunday, Dennis Feltgen, a National Hurricane Center spokesman, said: “Everything that we had hoped wouldn’t happen but was forecasted is happening. We have a catastrophic, life-threatening flood event taking place over southeastern Texas, including the Houston metropolitan area. It’s bad now and it’s getting worse.”
Trump wrote a series of tweets Sunday morning congratulating officials and emergency workers for their response to the torrential rain and flooding.
“Many people are now saying that this is the worst storm/hurricane they have ever seen,” he wrote in one tweet. “Good news is that we have great talent on the ground.”
The Weather Service issued repeated flash flood warnings throughout Saturday night, and dry city streets turned to speeding rivers in a matter of minutes. Emergency lines in the city were soon filled with people stranded on highways, and residents began sending desperate tweets directly to officials.
City officials urged flooded residents to head to their roofs, not their attics, to avoid being trapped.
On Sunday, the National Guard swarmed Houston, turning to high-water vehicles to make rescues. Stranded residents mounted the backs of some soldiers, who waded through thigh-high waters to take evacuees to trucks that would drive them to safety.
At midday, nine National Guard vehicles were parked along a stretch of Interstate 610. Soldiers in life jackets and camouflage pants were scrambling into a boat to make rescues nearby, and they expected to be busy for hours.
Harris County officials asked the public to contribute boats and high-water vehicles, which they said were desperately needed to help rescue people before nightfall.
Tom Bartlett and Steven Craig pulled a rowboat on a rope through chest-deep water for a mile to rescue Bartlett’s mother in west Houston. It took them 45 minutes to reach the house. Inside, the water reached halfway up the walls.
Marie Bartlett, 88, waited in her bedroom upstairs.
‘‘When I was younger, I used to wish I had a daughter, but I have the best son in the world,’’ she said. ‘‘In my 40 years here, I’ve never seen the water this high.’’
Houston’s main convention center was opened as a shelter.
Gillis Leho arrived there soaking wet. She said she awoke Sunday to find her downstairs flooded. She tried to move some belongings upstairs, then grabbed her grandchildren. ‘‘When they told us the current was getting high, we had to bust a window to get out,’’ Leho said.
William Cain sought shelter after water started coming into his family’s apartment and they lost power. ‘‘I live in a lake where there was once dry land,’’ he said.
Some people used inflatable beach toys, rubber rafts, and air mattresses to get to safety. Others waded while carrying trash bags stuffed with belongings and small animals in coolers.
Houston Mayor Sylvester Turner urged drivers to stay off flooded roads to avoid adding to the number of those stranded.
“‘We have several hundred structural flooding reports. We expect that number to rise pretty dramatically,’’ he said.
The Coast Guard deployed five helicopters and asked for additional aircraft.
It was the fiercest hurricane to hit the United States in 13 years and the strongest to strike Texas since 1961’s Hurricane Carla, the most powerful Texas hurricane on record. It came ashore Friday about 30 miles northeast of Corpus Christi with 130 mile-per-hour winds.
Harvey weakened Saturday to a tropical storm. On Sunday, it was virtually stationary 25 miles northwest of Victoria, with maximum sustained winds of about 40 miles per hour, the hurricane center said.
Rainfall of more than 4 inches per hour resulted in water levels higher than in any recent floods and higher than during Tropical Storm Allison in 2001, said Jeff Linder of the Harris County flood control district.
The deteriorating situation was bound to provoke questions about conflicting advice given by the governor and Houston leaders before the hurricane.
The governor urged people to flee from Harvey’s path, but Mayor Turner issued no evacuation orders and told everyone to stay home.
The governor refused to point fingers on Sunday.
‘‘Now is not the time to second-guess the decisions that were made,’’ Abbott, a Republican, said. ‘‘What’s important is that everybody work together to ensure that we are going to, first, save lives and, second, help people across the state rebuild.’’
The mayor, a Democrat, defended his decision, saying there was no way to know which parts of the city were most vulnerable.
‘‘If you think the situation right now is bad, and you give an order to evacuate, you are creating a nightmare,’’ Turner said, citing the risks of sending 2.3 million inhabitants onto the highways at the same time.
Material from the Associated Press, Washington Post, and New York Times was used in this report.