CORPUS CHRISTI, US - President Donald Trump flew into storm-ravaged Texas Tuesday in a show of solidarity and leadership in the face of the deadly devastation wrought by Harvey - as the battered US Gulf Coast braces for even more torrential rain.

Four days after Harvey slammed onshore as a monster Category Four hurricane, turning roads to rivers in America’s fourth-largest city, emergency crews are still racing to reach hundreds of stranded people in a massive round-the-clock rescue operation.

Eager to strike a unifying tone as the country faces the first natural disaster of his presidency, Trump landed with first lady Melania in the coastal city of Corpus Christi, which bore the full brunt of Harvey’s fury, for a briefing by state and federal officials leading the relief effort.

Emerging from the meeting held inside a local fire house, Trump climbed up on a ladder for an impromptu address to the mix of supporters and banner-waving protesters gathered outside.

“We love you, you are special, we are here to take care of you,” the president called out. “It’s historic, its epic, but I tell you, it happened in Texas - and Texas can handle anything.”

Trump earlier expressed hope the Harvey response would come to be seen as a textbook case.

“We want to be looked at in five years, in 10 years from now as, this is the way to do it,” he said.

The US leader was not planning to visit Houston - swathes of which remain under water - and his spokeswoman said his schedule would be fine-tuned to avoid disrupting ongoing recovery efforts.

But he was nevertheless seeking to make a political statement, learning from the mistakes of former Republican leader George W. Bush, whose response to Hurricane Katrina - which walloped New Orleans exactly 12 years ago - was widely seen as botched.

More than 8,000 people have been driven into emergency shelters across the Lone Star State, and hundreds more still await rescue.

“We’re Trumponites. I trust he’s going to take care of us,” said Darla Fitzgerald, a 58-year-old nurse based in a Red Cross shelter in Winnie, a town east of Houston, where the rain fell heavily Tuesday.

Ray Henrichson, a white-haired 74-year-old shelter volunteer, was equally upbeat. “I think it’s nice that he’s coming,” she said.

“He’ll probably fly around in a helicopter and see some flooded lands which we saw on the way driving here,” she said. “It is pretty dramatic.”

Harvey is known to have left at least three people dead so far, with six more deaths potentially tied to the storm, and officials warned the danger has far from passed.

Rising floodwaters breached a levee in Brazoria County south of Houston, with officials urging residents of the 50 homes in the immediate vicinity to leave immediately.

“The levee at Columbia Lakes has been breached!!” the county government tweeted. “GET OUT NOW!!”

The US Army Corps of Engineers has already moved 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.

With neighboring Louisiana squarely in the storm’s path, Harvey, now a tropical storm, is pressing eastward and is expected to make landfall again late Tuesday or early Wednesday.

Residents of low-lying New Orleans - which bore the brunt of Katrina’s wrath in 2005 - are bracing for heavy rain and flash floods.

“The single greatest threat continues to be the rainfall,” Dennis Feltgen, a spokesman for the Miami-based National Hurricane Center, told AFP, describing the situation as “catastrophic.” “This is not over,” he said.

The National Weather Service tweeted Tuesday that Harvey appears to have broken a US record for most rain from a single tropical cyclone, with 49.32 inches (125.27 centimeters) recorded at a gauge southeast of the city.

The Texas bayou and coastal prairie rapidly flooded after Harvey struck the coast on Friday, but the region’s sprawling cities where drainage is slower were worst hit.

Highways were swamped and homes were rendered uninhabitable, with power lines cut and dams overflowing, sparking massive floods across Houston - a city of 2.3 million people - and its wider metropolitan area of six million.

Houston can expect two to four more inches of rain as the storm moves away, but flooding will likely linger through the week, meteorologist Eric Holthaus told AFP.

In New Orleans, as of Tuesday morning, two inches of rain had already fallen over the city famous for its jazz music and Cajun cuisine - but particularly vulnerable because it lies below sea level.

“It is really sort of a wild card right now,” Holthaus said. “There are some forecasts for up to 10 inches of rain over the next 36 hours or so for New Orleans. I would definitely not be surprised if it became more than that.”

Federal officials estimate that up to half a million people in Texas will ultimately require some form of assistance - but for now the focus remains immediate disaster relief, with many lives still at stake.

“Recovery is a slow process,” Brock Long, the head of the Federal Emergency Management Agency, said as he welcomed briefing Trump in Corpus Christi along with Texas Governor Greg Abbott.

“We’ve got a long way to go,” Long said.