The Republican leader and First Lady Melania Trump will meet first responders and local officials in central Texas's Hill Country, a week after heavy rainfall and an overflowing river swept away houses, trees, cars and people.

They were due around midday in Kerrville, a city in the worst-affected Kerr County where at least 96 people died.

"I would have done it today, but we'd just be in their way," Trump told reporters when asked on Sunday about visiting the impacted communities.

The urgent search for more than 170 missing people, including five girls who were at summer camp, entered the eighth day as rescue teams combed through mounds of debris and mud.

But with no live rescues reported this week, worries have swelled that the death toll could still rise.

Trump has brushed off questions about the impact of his cuts to federal agencies on the response to the flood, which he described as a "100-year catastrophe" that "nobody expected."

On Thursday, Homeland Security Department head Kristi Noem defended the immediate response as "swift and efficient."

But she previously said Trump wanted to "upgrade the technologies" of the "ancient" weather warning system.

- FEMA questions -

The floods, among America's deadliest in recent years, have also reopened questions about Trump's plans to phase out disaster response agency FEMA in lieu of greater state-based responsibility.

FEMA began its response to the Texas flash floods over the weekend after Trump signed a major disaster declaration to release federal resources.

But the president has so far avoided addressing questions about its future. Noem insisted FEMA should be "eliminated" in its current form at a government review meeting on Wednesday.

Officials in Kerr County, which sits astride the Guadalupe River in an area nicknamed "Flash Flood Alley," said at least 36 children were killed in the flash floods that struck at the start of the Fourth of July weekend.

Details have surfaced about reported delays of early alerts at a local level that could have saved lives.

Experts say forecasters did their best and sent out timely and accurate warnings despite the sudden weather change.

White House Press Secretary Karoline Leavitt also defended National Weather Service (NWS) alerts as "early and consistent."

- Special session -

Kerr County Sheriff Larry Leitha said "it was between 4:00 or 5:00 (am) when I got notified" of incoming emergency calls.

ABC News reported Thursday that at 4:22 am on July 4, a firefighter in Ingram, upstream of Kerrville, had asked the Kerr County Sheriff's Office to alert residents of nearby Hunt to the coming flood.

The network said its affiliate KSAT obtained audio of the call, and that the first alert did not reach Kerr County's CodeRED system for a full 90 minutes.

In some cases, it said, the warning messages did not arrive until after 10:00 am, when hundreds of people had already been swept away by raging waters.

The flooding of the Guadalupe River was particularly devastating for summer camps on its banks, including Camp Mystic, where 27 girls and counselors died.

Five other Mystic campers and a counselor remain missing.

Governor Greg Abbott has scheduled a special session of the Texas Legislature to discuss the disaster, beginning July 21.

Kerrville Police Sergeant Jonathan Lamb said the session would be "a starting point" for reviewing ways to improve warning systems for weather events.