More people have been forced out of their homes nearly a week after Hurricane Harvey, as heavy rain hit Louisiana and knocked out the entire drinking water system in a Texas city of almost 120,000 people.

Meanwhile, the mayor of Houston pleaded for more high-water vehicles and more search-and-rescue equipment as the US’s fourth-largest city continued looking for any survivors or bodies that might have somehow escaped notice in flood-ravaged neighbourhoods.

Sylvester Turner also asked the Federal Emergency Management Agency (FEMA) to provide more workers to process applications from thousands of people seeking government help.

Harvey victims expect the FEMA to work “with the greatest degree of urgency”, Mr Turner said.

The mayor said he will request a preliminary financial aid package of 75 million dollars (£58 million) for debris removal alone.

The remnants of the storm were dying as they pushed deeper inland but remained powerful enough to raise the risk of flooding as far north as Kentucky.

More than 1,500 people were staying at shelters in Louisiana and that number was climbing as more people evacuate from flood-ravaged communities in Texas.

The state opened a seventh shelter on Friday in Shreveport for up to 2,400 people, said Shauna Sanford, a spokeswoman for Louisiana governor John Bel Edwards.

The city of Beaumont, near the Texas-Louisiana line, was evacuating and trying to bring in enough bottled water for people who stayed behind after a water pumping station was overwhelmed by the swollen Neches River.

The search for survivors and victims continues in HoustonThe search for survivors and victims continues in Houston (Ryan Pelham/AP)

In Houston, officials turned their attention to immediate needs such as finding temporary housing for those in shelters, but also to the city’s long-term recovery, which will take years and billions of dollars.

Authorities raised the death toll from the storm to 39 late on Thursday, while rescue workers conducted a street-by-street search of tens of thousands of Houston homes that rescuers began on Thursday.

The latest statewide damage surveys revealed the staggering extent of the destruction.

A car is submerged due to Tropical Storm Harvey in the north end of BeaumontA car is submerged due to Tropical Storm Harvey in the north end of Beaumont (Ryan Pelham/AP)

An estimated 136,000 structures in Harris County, or 10% of all structures in the county database, were flooded, according to the flood control district for the county, which includes Houston.

Jeff Lindner, a meteorologist for the agency, called that a conservative estimate.

It is 36,000 more homes than were flooded by Tropical Storm Allison in 1989, the area’s previous epic flood.

Where Storm Harvey is likely to go nextWhere Storm Harvey is likely to go next (PA Graphics)

The Texas Department of Public Safety said more than 37,000 homes were heavily damaged and nearly 7,000 were destroyed, figures that did not include the tens of thousands of homes with minor damage.

About 325,000 people have already sought federal emergency aid in the wake of Harvey.

More than 57 million dollars (£44 million) in individual assistance has already been paid out, FEMA officials said.

Houston fire chief Sam Pena said his department had responded to nearly 16,000 calls since the storm hit on Saturday, more than 7,600 of them for water rescues.

The search for more survivors and bodies began on Thursday when more than 200 firefighters, police officers and members of an urban search-and-rescue team fanned out across the Meyerland neighbourhood.

“We don’t think we’re going to find any humans, but we’re prepared if we do,” said district chief James Pennington, of the Houston Fire Department.