A record 30in of rain (75cm) has already fallen on the city of Houston in the wake of Hurricane Harvey, turning roads into rivers.
But forecasters say that number could nearly double later this week.
On Monday President Donald Trump also approved an emergency declaration for neighbouring Louisiana.
Harvey made landfall as a category-four hurricane late on Friday, bringing flooding described by officials as "unprecedented". It was later downgraded to a tropical storm.
Up to 2,000 people have been rescued in and around Houston, the fourth-largest city in the US, where about 6.6m people live in the metropolitan area.
The area is expected to have received a year's rainfall within a week. Five people are reported dead. Helicopters have plucked victims from rooftops.
Governor Greg Abbott has activated the entire Texas National Guard - some 12,000 so-called "civilian soldiers" - to assist national forces in search and rescue operations.
Officials say 30,000 people are expected to be housed in emergency shelters.
"Catastrophic and life-threatening flooding will continue across south-eastern Texas," the National Hurricane Center said on Monday.
"Additional rainfall accumulations of 15 to 25 inches are expected".
Meanwhile, army engineers have begun releasing water from two dams controlling water flowing along a major river into the heart of Houston.
Officials said they were opening the Addicks and Barker dams to stop water spilling into neighbouring communities, but that this could cause further damage down the Buffalo Bayou.
Photo caption: The water rose quickly trapping residents of La Vita Bella care home