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 the total rainfall could nearly double later this week.
US President Donald Trump has promised swift action to help those affected. He is due to visit Texas on Tuesday.
“Recovery will be a long and difficult road and the federal government stands ready, willing and able to support that effort,” he said.
He said he was dealing with Congress on funding, warning “it’s going to be a very expensive situation”.
President Trump has 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.
More than 3,000 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. Helicopters have plucked victims from rooftops.
At least nine people are reported to have died in incidents related to the storm, Texan officials say.
Six members of the same family died trying to flee rising floodwaters, relatives told US media, but the incident has not been confirmed.
Governor Greg Abbott has activated the entire Texas National Guard-about 12,000 so-called “civilian soldiers” – to assist national forces in search and rescue operations.
The area is expected to have received a year’s rainfall within a week.
Officials expect half a million disaster victims to seek assistance in Texas and 30,000 people 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”.
Let’s continue to #prayforhouston