Donald Trump is expected to visit Texas today, while parts of Louisiana are also preparing for potential flooding
Officials in Houston have warned the number of deaths from Tropical Storm Harvey could rise dramatically once devastating floodwaters have receded.
At least nine people have been killed by the slow-moving storm in Texas, but many others have been reported missing by worried loved ones.
Six members of the same family are feared dead after their van was submerged by a strong current as they tried to flee the storm.
Samuel Saldivar was trying to drive his elderly parents and his grandchildren to safety when the van was engulfed by violent floodwaters.
Although he managed to climb out of a window, no one else managed to escape - including four siblings aged between six and 16.
The coastguard has told the family they will not be able to search for the bodies until the water recedes.
Crews in Texas remain overwhelmed by thousands of rescue calls - and with further rain expected in the coming days, the authorities are worried the worst is yet to come.
Houston police chief Art Acevedo said: "We know in these kind of events that, sadly, the death toll goes up historically.
"I'm really worried about how many bodies we're going to find."
Parts of Houston, America's fourth-largest city, have seen 76cm of rainfall so far - and a further 61cm is forecast.
According to the Army Corp of Engineers, Harvey is generating an amount of rain that would normally be seen only once in more than 1,000 years.
Police have plucked more than 3,000 people from flooded neighbourhoods across the city, with the coastguard's boats and helicopters rescuing another 3,000.
More than 1,000 calls requesting assistance are being made to the coastguard every hour.
The amount of water in Houston is so unprecedented that the National Weather Service has had to update its official rainfall maps, introducing new colours representing higher amounts to accurately record the torrential downpours.
Southwestern parts of Louisiana are also preparing for potentially disastrous flooding, and hundreds of people have already been evacuated from chest-deep water after a heavy band of rain inundated Lake Charles on Monday night.
Although the damage will be nothing compared to the destruction wrought in Texas, the storm has revived painful memories for the survivors of Hurricane Katrina.
One of the five deadliest hurricanes in US history, Katrina caused damage in excess of $100bn when it battered New Orleans in 2005.
Donald Trump says the recovery operation following Harvey will be "very expensive", but has expressed confidence that Congress will act swiftly to pass a multibillion-dollar aid package to help victims.
Mr Trump said he would speak to the US Congress about boosting emergency funds.
He said: "We want to take care of the people of Texas and Louisiana when that happens - we'll see what happens with the flow, the flow seems to be heading towards Louisiana right now, as we speak - we'll be there for the people of Louisiana also."
He added that recovery from the storm's damage would be a "long and difficult road".
He is expected to travel to Texas on Tuesday to survey the damage, in what is the first major natural disaster of his White House tenure.