The 911 emergency line has received more than 75,000 calls, but city officials urged residents facing life-threatening storm water floods to remain on the line and trust that help will come.
Outside of Houston, the first death from Harvey was confirmed in a coastal community in Aransas County.
Many residents have been relying on mobile phones and social media to keep in touch with loved ones and to coordinate rescues during the massive storm that made landfall this weekend. They're also staring down a weather forecast for the evening that doesn't look promising as Harvey looks to regain power in the Gulf of Mexico and return for another crack at Houston.
Regina Costilla, 48, said she and her 16-year-old son had been rescued from their home by a good Samaritan with a boat.
"My heart goes out to my hometown, Houston, and I remain in constant prayer for those affected and for the rescuers who have been so fearless and determined to do so much to help", she said. "We are still on tornado and flash-flood watch", said Ms John, who stocked up on water after going to five grocery stores.
CATASTROPHIC flooding overwhelming Houston and other parts of Texas will worsen in the coming days and then be slow to recede once Hurricane Harvey finally moves on, the director of the National Weather Service in the United States has warned.
That amounts to about a year's worth of rain and there are also threats of flooding extending into neighboring Louisiana.More news: North Florida, South Georgia stuck between two tropical systems
"I think you're going to see very rapid action from Congress, certainly from the President", Trump said about federal funding to help the recovery effort.
Trump will travel to Texas on Tuesday to survey some of the damage.
President Donald Trump last week issued a declaration of emergency for Texas, which opens up additional federal funding for disaster relief.
Schools, airports and offices in the nation's fourth largest city were ordered shut yesterday as scores of roads turned into rivers and chest-high water filled neighbourhoods in the low-lying city that is home to about 2.3 million people.
The strategic engineering move, aimed at protecting the centre of Houston, could make already devastating flooding worse around thousands of homes.
"We're anticipating over 30,000 people being placed in shelters temporarily - to basically stabilize the situation and provide for their care".
And the size of the storm means it's not just Texas that must bear its blows.