At least 20 people have now died, with tens of thousands more homeless.
United States authorities have warned recovering from tropical storm Harvey is going to take years.
While more than 13,000 people have been rescued, nearly 50,000 homes have suffered flood damage.
The storm over the Gulf of Mexico has made landfall again near the Texas-Louisiana border after causing catastrophic flooding in Texas's biggest city, Houston, earlier this week.
The economic damage to south-east Texas is being estimated at at least US$50 billion.
Texas governor Greg Abbott says federal funding could surpass the aid distributed following Hurricane Katrina that hit New Orleans in 2005.
"My recollection is that the Katrina funding was well over $100 billion. I want to say it was over $125 billion. And so, if we go on a parallel standard, it should be far in excess of that amount."
Governor Abbott has also warned residents of the storm-hit areas that catastrophic flooding may continue for up to a week.
"The worst is not yet over for south-east Texas, as far as the rain is concerned. There will be ongoing challenges, both during the time that rain continues to fall as well as for approximately four days to a week to come. Let me mention specifically flooding conditions that will continue to be a challenge for people in the area."
Federal authorities say they have more than 230 packed shelters in Texas providing relief to more than 30,000 people.
Federal Emergency Management Agency director Brock Long says authorities are still trying to save lives before moving on to other matters.
He is pleading for understanding from those people affected.
"The operation right now is very clear: we're still in life-saving, life-sustaining mode. Not only are we performing, through our partners at the Coast Guard, those life-safety measures, but the life-sustainment mission is huge. It's going to grow. (This is) just to let the people of Texas know that we are supporting the efforts to provide mass care -- not only mass care, but also medical care -- to those who have been displaced. And we understand that this is going to be a frustrating and painful process. But we're trying to do everything we can."
Houston officials placed a night-time curfew on the city to try to prevent looting and other crime.
Houston mayor Sylvester Turner has called for people to comply with the restrictions.
"Quite frankly, no-one needs to be on the road, or out, from 10pm to 5am. But there are too many people from across our city, too many residents, that are out of their homes, and they are in shelters. And I don't want them to have to worry about someone breaking into their home, or looting, or doing anything of that nature, while they are away."
Almost 40 centimetres of rain has already fallen in some parts of Texas and Louisiana.
