US President George W Bush has declared Texas a federal disaster zone after Hurricane Ike battered the state with winds in excess of 110mph (175km/h).
Before weakening to a tropical storm, Ike flooded the coastline, ripped off roofs and caused extensive blackouts.
Rescuers in Galveston, where Ike made landfall, are checking on thousands of people who ignored an evacuation order.
Reports of deaths have not been confirmed, but a "worst-case scenario" did not occur, officials say.
Ike also damaged Houston, the fourth-largest city in the US.
A BBC correspondent who weathered the storm there described how ferocious winds ripped the glass from many of the city's skyscrapers.
Production has been suspended at 14 oil refineries and 28 natural gas processing plants that were in the storm's path.
'Not worst-case scenario'
By designating Texas a disaster zone, Mr Bush freed up millions of dollars in federal disaster aid to help those affected by the storm.
"The storm has yet to pass and I know there are people concerned about their lives," he said, speaking outside the White House after consulting emergencies officials.
"Some people didn't evacuate when asked. I've been briefed on the rescue teams there in the area.
"They're prepared to move as soon as weather conditions permit. Obviously, people on the ground there are sensitive to helping people and are fully prepared to do so."
Homeland Security Secretary Michael Chertoff said he had received information about a number of deaths as a result of the storm but could not yet confirm them.
"There will be a lot of rain and the rain will continue to cause flooding problems," he said, speaking in the US capital.
"The impact... was not quite as bad as the worst-case scenario, it was still substantial."
Swamped in Houston
Ike was downgraded to a tropical storm by the US National Hurricane Center at 1900 GMT, as it moved inland with top sustained winds of nearly 60mph (95km/h).
It is moving towards north-east Texas and is expected to reach western Arkansas on Saturday night local time.
A few hours after the storm passed through Houston, the BBC's Rajesh Mirchandani reported that his hotel was surrounded by water on three sides.
A small marina nearby was full of yachts capsized and sinking, with one boat flung on to an apartment complex.
In the island city of Galveston, rescuers began searches just a few hours after Ike made landfall at 0710 GMT, on Saturday.
Officials were encouraged by the fact that that the storm surge turned out to be much lower than forecast - 13.5ft (4m) after predictions of 20 to 25ft foot (6 to 7.5m).
But major roads were washed out near the town and the damage was still "immense", The Associated Press reports.
Police agencies say it could take days to get into the areas worst affected in Galveston and the extent of the damage may not be known for some time, our correspondent adds.
Earlier, Ike caused devastation in Cuba and Haiti, where hundreds of people have died several tropical storms over the last month.