US President Donald Trump receives a briefing on Tropical Storm Harvey relief efforts with Texas Governor Greg Abbott (R) at the Texas Department of Public Safety Emergency Operations Center in Austin, Texas, US, August 29, 2017. [Photo/Agencies]

HOUSTON - President Donald Trump visited Texas on Tuesday to survey damage from the first major natural disaster to test his leadership in a crisis, as record rainfall from Tropical Storm Harvey lashed Houston and tens of thousands of people fled deluged homes.

The slow-moving storm has brought catastrophic flooding to Texas, killing at least 12 people and paralyzing Houston, the America's fourth most populous city. Damage was expected to run well into the tens of billions of dollars, making it one of the costliest US natural disasters.

City officials were preparing to temporarily house some 19,000 people, with thousands more expected to flee the area as the flooding entered its fourth day and authorities found themselves running out of space in cramped shelters.

The Mayor of Houston imposed a 10 pm to 5 am curfew.

Nearly a third of Harris County was under water, an area 15 times the size of Manhattan, according to the Houston Chronicle newspaper. Forecasters warned the rain would continue through Thursday, badly straining the dams and drainage systems that protect the low-lying US energy hub.

Harris County officials warned 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.

Residents within 1.5 miles (2.4 km) of a chemical plant in Crosby were also ordered to evacuate due to the rising risk of an explosion.

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.

"This was of epic proportion. Nobody's ever seen anything like this," Trump said of Tropical Storm Harvey as he met with state and federal officials for a briefing at a Corpus Christi fire station.

The president said he was pleased with the response so far, but it was too soon to take a victory lap.

"We won't say congratulations. We don't want to do that.... We'll congratulate each other when it's all finished," he said.

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.

Harvey has drawn comparisons with Hurricane Katrina, which devastated New Orleans 12 years ago, killing 1,800 people and causing an estimated $108 billion in damage.

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, and Trump clearly was aiming to avoid a similar reaction.

Among the 12 confirmed fatalities as of Tuesday evening was a family of six and Houston Police Sergeant Steve Perez, a 34-year veteran of the force who apparently drowned while attempting to drive to work on Sunday, Police Chief Art Acevedo told reporters.

Acevedo said in an emotional press conference that Perez' family had urged him not to leave the house because of the dangerous flooding but the 60-year-old policeman told them, "We have work to do."

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.

Reuters