Donald Trump is traveling to Texas on Tuesday, as Harvey is expected to regain strength and bring floods to neighboring Louisiana.
Trump's trip is aimed at showing unity in the face of what he called the "terrible tragedy" wrought by monster storm Harvey's devastating rains.
The US president and his wife Melania are not expected to visit Houston, America's fourth largest city where rescuers are scrambling to reach hundreds of stranded people as Harvey appeared poised to strike again.
They will instead make stops further west, including hard-hit Corpus Christi, for briefings on relief efforts after catastrophic flooding crippled southeastern parts of the vast state, the country's second largest by size.
Tuesday officials from Harris County, which includes Houston, have raised the death total to 10.
"We are one American family," Trump said Monday, eager to present himself as a unifying figure as he faced the first natural disaster of his presidency — after seven months of leading a White House plagued by controversy, much of it self-generated.
He promised the federal government would be on hand to help Texas along the "long and difficult road to recovery" from the historic storm.
But officials warned the danger has not yet passed, with more families still stranded or packed into emergency shelters and the tropical storm once more gathering strength on the Gulf coast.
Trump has also declared a state of emergency in Louisiana, next in line for a downpour.
Houston Mayor Sylvester Turner said more than 8,000 people, soaked and desperate, had been brought to shelters in this city of more than six million.
Coast Guard Commander Vice Admiral Karl Schultz told CNN he had 18 helicopters in Houston, and — weather permitting — about 12 in the air at any one time, alongside those of the National Guard.
"If you can get to your roof, wave a towel. Leave a marking on the roof so helicopter crews can see you," he said, describing the volume of emergency calls as "staggering."
Harvey hit Texas on Friday as a Category Four hurricane, tearing down homes and businesses on the Gulf Coast before dumping an "unprecedented" amount of rainfall inland.
The Texas bayou and coastal prairie rapidly flooded, but the region's sprawling cities — where drainage is slower — were worst hit.
Highways were swamped and residential streets were rapidly rendered uninhabitable, with power lines cut and dams overflowing.
The US Army Corps of Engineers began to open the Addicks and Barker dams — under pressure from what the agency has dubbed a "thousand-year flood event" — to prevent a catastrophe on the outskirts of Houston.
Latitia Rodriguez was rescued along with her husband, children and grandchildren by the Williamson County police department, negotiating the flooded Route 90 in boats.
"We have to evacuate. We have too many kids. So we had to save our babies," she told AFP. "There's a lot of people over there. We would like to help everybody but we can't. We have our own kids."
Meanwhile, the disaster is far from over: Harvey has turned back on itself and is hovering on the Gulf Coast, sucking up more rain and threatening a new landfall on Wednesday.
And only after the storm will come clean-up and recovery.
"We actually anticipate that as many as a half a million people in Texas will be eligible for and applying for financial disaster assistance," Vice President Mike Pence told KHOU Radio in Houston.
"We know it's far from over."
The Houston branch of the National Weather Service said Tuesday that August 2017 was the wettest month on record, accumulating a total 36.68 inches.
The city's average annual rainfall is 49.77 inches.
Rescue efforts on the outskirts of town appeared to be disjointed.
In Williamstown County, a police boat sitting on a flooded highway tried to rescue people but had nowhere to take them because no emergency vehicles could collect them from a dropoff location.
Roughly 50 people needed rescuing, 12 of whom had non-life-threatening medical conditions. Rescuers had to leave them there despite multiple requests for emergency vehicles that never came.
Many people living in smaller communities by the coast were also driven from their homes.
Robert Frazier, a 54-year-old foreman mechanic, left his home in La Porte, south of Houston, with his wife Judy on Sunday and made it as far as a motel on the road toward Louisiana — which is still in Harvey's path.
His wife said she could only pray the rain would stop, after leaving home with just two sets of clothes, their medicine and their dog.
"We're trapped," Frazier told AFP after trying to return home for some of his abandoned possessions but found that the highway was cut.
"I haven't been through nothing like this," he said.
by Katie Schubauer/AFP