Tropical storm Harvey is not going anywhere fast, the slow-moving nature of the storm causing further havoc and catching authorities by surprise.
Thousands of people across the state have been affected by the intense weather conditions, which have brought the city of Houston to a standstill.
Among the dead is a Houston police officer.
The city's police chief, Art Acevedo, relayed the news in an emotional press conference.
"This morning at 8am, the dive team was out there again, which was their number one priority, and, within 20 minutes, they found him. Unfortunately, in the darkness, Sergeant Perez drove into an underpass that's about 16-and-a-half feet (5m) deep, drove into the water, and he died in a flood drowning-type event."
Residents in Texas's south-eastern Harris County were told to leave as workers released water to alleviate pressure on reservoirs built to handle drainage waters.
They had begun to overflow.
The Pentagon, which would usually be in recovery mode by this stage, says it is instead preparing for further calls for help as the storm continues to sit over the Gulf of Mexico.
Officials say shelters are struggling to cope with the demand, with the main shelter housed in a downtown convention centre at nearly double its capacity.
Houston mayor Sylvester Turner has appealed for greater resources.
"The reality is that not only are we providing shelter for Houstonians, but we are also providing shelter for people who are coming from outside the city of Houston, who have been directly impacted by the storm. We're not turning anyone away, but it does mean that we need to expand our capabilities and our capacity."
At least one site south of Houston has had its rainfall record broken by Harvey, recording 1.25 metres of precipitation since the storm began.
Around 3,500 people have already been rescued in the Houston area, and police say they are seeing instances of looting.
The crisis has drawn comparisons to 2005's Hurricane Katrina, when then-president George W. Bush faced criticism over his response as almost 2,000 people died.
Speaking in Corpus Christi, where Harvey first made landfall, US president Donald Trump says he wants to set a precedent for disaster management.
"This was of epic proportion. Nobody's ever seen anything like this. And I just want to say that working with the governor and his entire team has been an honour for us. So, Governor, again, thank you very much. And we won't say congratulations, we don't want to do that, we don't want to congratulate. We will congratulate each other when it's all finished."
Mr Trump planned to head next to the state's capital, Austin, because he could not reach Houston in the hazardous conditions.
The United Nations says climate change could be responsible for the hurricane's ferocity.
It says rising temperatures are likely to blame for increased humidity and heavier rainfalls.
Rebuilding efforts are expected to take years and cost billions of dollars.
Houston resident Jose Gonzalez says the mental scars will take longer to heal.
"It's bad, man. It's terrible. It's really bad. The water is way ... it's almost, I want to say, up to my knees, just about, but it's really bad over there. Nobody expected this."
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