(Updates death toll, storm position, adds Trump quote)
HOUSTON, Aug 29 (Reuters) - U.S. President Donald Trump arrived in Texas on Tuesday to survey the damage of Tropical Storm Harvey, the biggest natural disaster of his tenure, as record-setting rainfall lashed Houston and tens of thousands of people fled flooded homes.
The slow-moving storm has brought catastrophic flooding to Texas, killing at least 11 people and paralyzing Houston, the fourth most-populous U.S. city. City officials were preparing to shelter up to 19,000 people, with thousands more expected to flee the area as the flooding entered its fourth day.
A wide swath of Houston and its surrounding suburbs were under water and forecasters warned the rain would continue through Thursday, stressing the dams and drainage systems that protect the low-lying U.S. energy hub.
Officials in Harris County, where Houston is located, warned area residents to evacuate as they released water from overflowing reservoirs to alleviate pressure on two dams, a move that would add to flooding along the Buffalo Bayou waterway that runs through the area.
Trump, speaking in Corpus Christi near where Harvey first came ashore last week as the most powerful hurricane to strike Texas in more than 50 years, said he wanted the relief effort to stand as an example of how to respond to a storm.
"We want to do it better than ever before," he said.
Trump later spoke to a crowd of people affected by the storm.
"This storm, it's epic what happened. But you know what, it happened in Texas and Texas can handle anything," Trump said, before waving a Texas state flag over the crowd, standing on a stepladder near a fire truck.
Harvey has drawn comparisons with Hurricane Katrina, which devastated New Orleans 12 years ago, killing 1,800 people. Former President George W. Bush was widely criticized for his administration's handling of the response to that disaster, taking a heavy toll on public support of his administration.
Trump clearly was aiming to avoid a similar reaction.
An 11th death was reported on Tuesday. A Houston officer drowned in his patrol car, the Houston Chronicle reported, citing three Houston Police Department officials.
Some 3,500 people have been rescued from high waters in the Houston area with police, firefighters and National Guard troops continuing to try to locate those marooned in high waters.
Large numbers of civilians also formed ad hoc rescue groups, many using boats to pluck neighbors from flooded homes.
Gloria Stilwell, 44, who described herself as a stay-at-home mom, said she agreed with Trump's assessment that Houstonians were well equipped to handle the storm.
"I totally agree with him. Texas can definitely handle it," Stilwell said as she registered to volunteer at a shelter. "I've lived here since 1980, through plenty of hurricanes. Texans have always banded together."
Nurse Lisa Ike, 39, was less impressed.
"Texas can handle anything? I just lost my house and three cars. We need help," Ike said, after being shown Trump's comments.
She said she had not voted in the presidential election and said she had not yet made up her mind about Trump, adding, "My opinion will be made by how he handles this situation."
The storm broke rainfall records for the continental United States, with one site south of Houston recording 49.2 inches (1.25 meters) of precipitation since the storm's start. The rainfall about what the region typically sees in a year and exceeds 48 inches (1.22 meters) recorded in 1978.
Multiple looters were arrested overnight, police said.
Harvey has roiled energy markets and wrought damage estimated to be in the billions of dollars, with rebuilding likely to last beyond Trump's four-year term in office.
After Corpus Christi, Trump was headed to the state capital Austin to meet with officials. Houston was not on his itinerary because much of it is impassable.
About 9,000 evacuees were staying at Houston's George R. Brown Convention Center and Houston Mayor Sylvester Turner said his office had asked the Federal Emergency Management Agency for assets to allow the city to shelter another 10,000 people.
"I'm just trying to stay strong," said Julio Gamez, 35, who evacuated to the center on Saturday night with his wife after floodwaters rose to within a foot (30 cm) of his roof. "We've lost everything. But at least we're safe."
Other shelters were set up in Dallas, about 250 miles (402 km) to the north, for about 8,000 people, and Austin, 160 miles (258 km) west, to take in 7,000 people. The Red Cross said it had 34,000 cots in the region and enough food for that many people.
LOUISIANA ALSO THREATENED
Harvey was also drenching Louisiana 12 years after Hurricane Katrina hit the state and killed 1,800 people.
The slow-moving storm's center was in the Gulf of Mexico about 93 miles (150 km) southeast of Houston by midday Monday. It was likely to remain just off the coast of Texas through Tuesday night before moving inland late Tuesday or early Wednesday, according to the U.S. National Hurricane Center.
Harvey was expected to produce another 6 to 12 inches (15 to 30 cm) of rain through Thursday over parts of the upper Texas coast into southwestern Louisiana.
The Gulf of Mexico is home to half of U.S. refining capacity. The reduction in supply led gasoline futures to hit their highest level in two years this week as Harvey knocked out about 16 percent of total U.S. refining capacity, based on company reports and Reuters estimates.
(Additional reporting by Gary McWilliams, Ernest Scheyder and Erwin Seba in Houston; Andy Sullivan in Rockport, Texas; Jon Herskovitz in Austin; Steve Holland in Corpus Christi, Texas; Bernie Woodall in Fort Lauderdale, Florida; and David Gaffen in New York; Writing by Scott Malone; Editing by Bill Trott and Lisa Shumaker)