Update 9.14pm: President Donald Trump has offered reassurances to Texans who felt the wrath of Storm Harvey, promising residents during a visit to the state: "We are going to get you back and operating immediately."
Starting his visit in wind-whipped but sunny Corpus Christi, Mr Trump's motorcade passed broken trees and knocked down signs as it made its way to a firehouse for a briefing with local officials.
"This was of epic proportion," the president declared as he pledged to provide recovery assistance. "We want to do it better than ever before. We want to be looked at in five years, in 10 years from now as, 'This is the way to do it'."
Afterwards, Mr Trump stood between two fire engines and spoke to a crowd of hundreds of people gathered outside.
"What a crowd. What a turnout," he said, thanking Texas governor Greg Abbott and senators Ted Cruz and John Cornyn.
"This is historic. It's epic what happened, but you know what, it happened in Texas, and Texas can handle anything."
White House press secretary Sarah Huckabee Sanders told reporters travelling with Mr Trump that the president's visit was focused on coordination among different levels of government and laying the groundwork for what is expected to be a lengthy recovery effort.
"The president wants to be very cautious about making sure that any activity doesn't disrupt the recovery efforts that are still ongoing," she said aboard Air Force One shortly before it touched down in Corpus Christi.
Mr Trump travelled with first lady Melania Trump and Cabinet secretaries who will play key roles in the recovery. Some people lining roads near the airport held American flags and waved as the motorcade passed.
The president, who wore a white cap that said "USA", was briefed in Corpus Christi on relief efforts.
Then he headed to Austin to meet state officials at the emergency operations centre. Mrs Trump, who traded in her usual stiletto heels for a pair of white trainers, wore a black baseball cap that read "FLOTUS", an acronym for "first lady of the United States".
The Cabinet secretaries were to meet with their Texas counterparts during Mr Trump's visit.
"That's a big part of what today will be about, the coordination between local, state and federal officials and laying the groundwork for the recovery effort," Ms Sanders said.
Mr Trump has embraced the role of guiding the nation's response to Harvey, which made landfall along the Gulf Coast on Friday night as a Category 4 storm near Corpus Christi, and moved north-east along the Texas coast over Houston.
The storm has dumped more than 30 inches of rain in parts of Texas and authorities have rescued thousands of people left stranded by the storm.
Mr Trump's vow of swift action on billions of dollars in disaster aid is at odds with his proposed budget, which would eliminate the programme that helps Americans without flood insurance rebuild their homes and cuts grants to states that would allow them to take long-term steps to reduce the risk of flooding before disaster strikes.
Vice president Mike Pence said Harvey's relentless nature and size were "frustrating".
In a pair of interviews on Tuesday with radio stations serving Corpus Christi and San Antonio, Mr Pence warned that life-threatening flooding will continue and urged listeners to continue to follow instructions from local authorities.
He said he and his wife, Karen, would visit the region later this week. And Mr rump plans to return to the region later in the week.
Mr Trump saw a largely functioning Corpus Christi, a city of 325,000, where damage was minimal.
Power has largely been restored, particularly in commercial areas. Some restaurants have reopened and stores are restocked. Hotels are jammed with evacuees from hard-hit areas to its north-east, including Houston.
Residents have been advised to boil drinking water because authorities cannot guarantee the integrity of the city's lead and steel water system.
Earlier: A pair of reservoir dams that protect central Houston and a suburban levee have started overflowing, adding to the rising floodwaters from Storm Harvey that have crippled the city after five days of rain.
US President and First Lady Donald and Melania Trump have arrived in Texas so they can see the damage caused by Hurricane Harvey. They are currently in the coastal city of Corpus Christi - where the storm first made landfall.
Engineers began releasing water from the Addicks and Barker reservoirs on Monday to ease the strain on the 70-year-old dams, but the releases were not enough to relieve the pressure after one of the heaviest downpours in US history, the Army Corps of Engineers said.
Both reservoirs are at record levels and the release of water means more homes and streets will flood, with some homes inundated for up to a month, said Jeff Lindner of Harris County Flood Control District.
The county is trying to determine where the water will go, Mr Lindner added.
Meanwhile, Brazoria County authorities posted a message on Twitter warning that the levee at Columbia Lakes, south of Houston, had been breached and telling people to leave the area.
Authorities said residents had been warned that the levee would overflow at some point and a mandatory evacuation order was given on Sunday.
More than 17,000 people are seeking refuge in Texas shelters, the American Red Cross said, and the number looks certain to grow.
Calls for rescue have so overwhelmed emergency teams that they have had little time to search for bodies, and officials acknowledge that fatalities could soar once the floodwaters start to recede from one of America's most sprawling metropolitan centres.
More than four days after the storm ravaged the Texas coastline as a Category 4 hurricane, authorities had confirmed three deaths - including a woman killed when heavy rains dislodged a large tree on to her trailer home in the small town of Porter.
"We know in these kinds of events that, sadly, the death toll goes up, historically," Houston Police Chief Art Acevedo said. "I'm really worried about how many bodies we're going to find."
One Houston woman said she presumes six members of a family, including four of her grandchildren, died after their van sank into Greens Bayou in East Houston.
Virginia Saldivar said her brother-in-law was driving the van when a strong current took the vehicle off a bridge and into the bayou. The driver got out and urged the children to escape through the back door, Ms Saldivar said, but they could not.
"I'm just hoping we find the bodies," she added.
A spokeswoman for a Houston hotel said one of its employees disappeared while helping about 100 guests and workers evacuate the building.
The disaster is unfolding on an epic scale, with the nation's fourth-largest city mostly paralysed by the storm that parked itself over the Gulf Coast. With nearly 2ft more of rain expected on top of the 30in that has fallen so far in some places, authorities worried the worst might be yet to come.
The Houston metro area covers about 10,000 square miles, and is crisscrossed by about 1,700 miles of channels, creeks and bayous that drain into the Gulf of Mexico, about 50 miles to the south east.
Forecasters expect the storm to linger over the Gulf before heading back inland east of Houston some time on Wednesday. The system will then head north and lose its tropical strength.
Rescuers continued plucking people from inundated Houston neighbourhoods. Mayor Sylvester Turner put the number saved by police at more than 3,000, while the Coast Guard said it had also rescued more than 3,000 by boat and air and was taking more than 1,000 calls per hour.
Nearly 6,000 inmates displaced by flooding have been moved from prisons in the Houston area to other facilities in south and east Texas, according to the state Department of Criminal Justice.
A mandatory evacuation was ordered for the low-lying Houston suburb of Dickinson, home to 20,000, and questions swirled in Houston itself about why the mayor did not issue a similar evacuation order.
Mr Turner has inisisted that a mass evacuation of millions of people by car was a greater risk than enduring the storm.
By Tuesday morning, more than 9,000 people were at the city's largest shelter set up at the George R Brown Convention Centre - which originally had an estimated capacity of 5,000.
The Red Cross said volunteers made more space in part by pushing some camp beds closer together. A shortage of beds means some people will have to sleep on chairs or the floor.
Before the storm is gone, up to 20in more rain could fall, the National Weather Service said, meaning the flooding will get worse in the days ahead and the water will be slow to recede once Harvey finally moves on.