Rescuers searched painstakingly through flooded neighborhoods across southeastern Texas on Friday for people stranded by Hurricane Harvey's deluge as President Donald Trump asked Congress for $7.85 billion in federal disaster relief.

The storm, one of the costliest to hit the United States, has displaced more than one million people, with 50 feared dead from flooding that paralysed Houston, swelled river levels to record highs and knocked out the drinking water supply in Beaumont, Texas, a city of 120,000 people.

The Trump administration in a letter to Congress asked for a $7.85 billion appropriation for response and initial recovery efforts. White House homeland security adviser Tom Bossert told reporters on Thursday aid funding requests would come in stages as more became known about the impact of the storm.

Texas Governor Greg Abbott has said that his state may need more than $125 billion.

Bossert said the Trump administration wanted Congress to pass the disaster relief measure on its own and not add it to other measures, such as the effort to raise the debt ceiling.

Texas Governor Greg Abbott has said that his state may need more than $125 billion

The US government has a statutory limit on how much money it can borrow to cover the budget deficit that results from Washington spending more than it collects in taxes. Only Congress can raise that limit.

Trump plans a second visit to the region today.

Though the sun was out in Houston on Friday and water levels down in many areas, Mayor Sylvester Turner called for voluntary evacuations on the city's west side. He said already-flooded neighborhoods there may be in greater danger as the Army Corps of Engineers continues to release water into the adjacent Buffalo Bayou to prevent dam and levee failures.

About 130km to the east, the Neches River, which flows into Beaumont and nearby Port Arthur, was forecast to crest early today well above flood levels, the National Weather Service said.

The Sam Houston Parkway is still completely covered with Harvey floodwaters in Houston. Photo: ReutersThe Sam Houston Parkway is still completely covered with Harvey floodwaters in Houston. Photo: Reuters

"It (the Neches River) is about 2.1 metres above the record and it will continue to remain at or be near that high for about the next week. This flooding poses an ongoing threat," Texas Governor Abbott told reporters.

Rescue officials were still working to determine the scope of flooding, said Rodney Smith, deputy chief of the Cedar Hill, Texas, Fire Department.

The storm's impact played out in ways large and small, a full week after Hurricane Harvey slammed into the Texas coast as the strongest hurricane to hit the state in more than 50 years.

Harvey, which lingered around the Gulf of Mexico Coast for days, dumped unprecedented amounts of rain and left devastation across more than 480km of the state's coast.

A list of the dead put out by Harris County painted a grim picture of the storm's brutality, describing bodies found floating face down in floodwaters, lying in ditches or across fences. Many were unidentified.

Harvey came on the 12th anniversary of Hurricane Katrina, which killed about 1,800 around New Orleans.

Some 440,000 Texans have already applied for federal financial disaster assistance, and some $79 million has been approved so far, Abbott said.

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