Mr Trump, who visited Texas earlier this week will return to the state on Saturday - and may visit Louisiana, which has also seen serious flooding.
White House spokeswoman Sarah Sanders told reporters, "he'll pledge, proudly, $1 million of his own personal money to help the people of Texas and Louisiana."
It comes after Houston, America's fourth-largest city got relief as the raging waters receded.
Speaking from the coastal city of Corpus Christi US Vice President Mike Pence hailed rescuers and volunteers for their "compassion and concern."
"Every American should know that even in this difficult time and this disastrous storm, the very best are the people of Texas, and the very best are the people of America shining forth," he said.
In Beaumont, northwest of the coastal city of Port Arthur, the water system was down.
Brock Long, the head of the US Federal Emergency Management Agency (FEMA), said his agency was working with the state and the military to open water distribution points for those affected.
Indeed, military trucks fanned out, loaded up with bottled water, military backpacks and personnel ready to help.
The breakdown of the water system forced the evacuation of nearly 200 patients from a Beaumont hospital, some by military helicopters.
"We've practiced this many times before," hospital spokeswoman Mary Poole said.
"We're trying to keep them as close as possible," she said of the evacuated patients. "Part of the healing process is to be with your family."
Rescuers scour Texas for victims
One week after monster storm Harvey slammed into the Gulf Coast, rescue workers on Friday were scouring storm-ravaged southeast Texas for victims trapped in their flooded homes, even as some towns finally found slight relief as waters receded.
Emergency workers were staging dramatic rescues by air and water in Texas towns that were until now cut off by raging floodwaters unleashed by Harvey, which finally began moving inland after crashing into the region as a Category Four hurricane last Friday.
Thousands of rescuers and civilians eager to help battled difficult conditions to reach victims of the unprecedented flooding.
Homes are surrounded by floodwater after torrential rains pounded Southeast Texas following Hurricane and Tropical Storm Harvey (Getty Images) Source: Getty Images
"We felt we'd be alright. We were wrong," said Lonnie Givens, who refused to evacuate his one-story home in the town of Orange. Now, he and wife Missy have about four inches (10 centimeters) of water in the house and no power.
"We really got nowhere to go," Givens said.
His situation echoed those of many in Texas towns inundated by days of torrential rains, with highways still submerged and homes destroyed.
A hospital in the hard-hit town of Beaumont was forced to evacuate its patients, nearly 200 people, when the town's water supply went down.
Harvey has been blamed thus far for at least 38 deaths and tens of billions of dollars of damage. A lack of power also triggered twin blasts at a Texas chemical plant, but authorities said the danger was limited.
Meanwhile, Hurricane Irma had intensified into a Category 3 system, churning in open waters but heading straight toward the southern Caribbean, where it was forecast to reach early next week.
It was still too early to tell if the storm currently packing 115 miles (185 kilometers) per hour winds would impact Florida or the Gulf of Mexico, but anxiety was running high in the aftermath of Harvey's pummeling.
Homeland Security Adviser Tom Bossert estimated 100,000 homes had been affected by flooding -- some with eight feet (2.4 meters) of water or more -- and said the White House would ask Congress for emergency funds.
Related reading
Harvey deluges cities, displaces 1 million
'Out of harm's way'
Early Thursday, a pair of explosions rocked a flooded chemical plant in Crosby, a town of around 3,000 people some 25 miles (40 kilometers) northeast of Houston, sending a plume of smoke into the air.
Officials ordered residents living within 1.5 miles of the facility to evacuate amid concerns about the fumes emanating from the plant, which produces organic peroxides, compounds that can combust if not cooled to the right temperature.
The Environmental Protection Agency said it was reviewing data from an aircraft that surveyed the scene and had no indication that dangerous amounts of toxic materials have been released.
"We believe along with the local authorities that we've moved everyone out of harm's way, and that no one is in danger," Richard Rennard, a senior executive for French plant owner Arkema, told a news conference.
Fifteen sheriff's deputies who responded to the fire were briefly hospitalized.
Crosby resident Lane Averett, 59, told AFP at a church shelter in the town that he was worried about the animals he had left behind.
"I got a dog and three cats, and a calf shut up in the trailer where they can't get no water or feed or nothing," Averett said.
Up to $75 billion in damage
In Louisiana, authorities scrambled to safeguard their state from Harvey, whose onslaught evoked painful memories of Hurricane Katrina's deadly strike 12 years ago, but New Orleans escaped with minimal rain.
So far, parts of Texas have seen more than 50 inches (1.27 meters) of rain, while in Louisiana, the total neared 24 inches.
More than 30,000 people have found refuge in shelters across Texas, from the giant Houston convention center to small churches, according to FEMA.
In Houston, where Mayor Sylvester Turner issued a nighttime curfew to aid search efforts and thwart potential looting, the two major airports have reopened on a limited basis, signaling a slow return to normality.
In Texas, the storm damage is staggering - Enki Research put its "best estimate" cost at between $48 billion and $75 billion.
