Mandatory evacuation orders affected more than one million people, but there are fears for up to 90,000 people across Texas who officials say decided to brave out the storm.
In Galveston, an estimated 23,000 residents stayed behind.
President George W Bush, who earlier declared a federal emergency in Texas, said the federal and state authorities would conduct the recovery effort together, bringing in generators and ensuring water and ice supplies.
US Homeland Security Secretary Michael Chertoff is due to arrive in Texas on Saturday, weather conditions permitting, he added, speaking at the White House.
The US Environmental Protection Agency has waived federal clean air regulations for petrol sold in states affected by the storm, in an effort to reduce fuel disruption.
Ike has halted more than a fifth of US oil production, forcing 17 refineries in the Gulf of Mexico to shut down as a precaution.
Rain and debris
Jessica Willey, a journalist based in Galveston which lies on a small island off the coast of Texas, told the BBC it was the worst storm she had ever seen:
See the likely path of Hurricane Ike through the US
"The rain is coming sideways. Debris is flying through the air. Things are getting ripped off buildings every second, and flying through the air.
All emergency workers have been pulled off the streets until daybreak when a curfew will be lifted.
"We hope we will find the people who are left here alive and well," said Galveston mayor Lynda Ann Thomas.
There is widespread flooding, and a hospital there is under at least 9.8ft (3 metres of water). The city has lost power and a number of houses are reported to be on fire.
Residents of low-lying homes were warned they faced "certain death" if they stayed.
Haitian appeal
At 1300 GMT, Hurricane Ike was about 20 miles (30km) south-southeast of Huntsville, Texas, with top sustained winds of nearly 90mph (145km/h).
The BBC's John Hammond tracks the path of Hurricane Ike
It was due to pass through eastern Texas during the day, reaching western Arkansas on Saturday night, according to US National Hurricane Center.
US officials have warned as many as 100,000 homes in Texas could be affected by flooding.
Nearly 4.5 million people in the Houston-Galveston area are without electricity, a spokesman for power company CenterPoint Energy said.
The BBC's Rajesh Mirchandani in Houston reports that ferocious winds and rain have been lashing at his hotel for 10 hours.
"We are largely trapped here," he said. "The power went out five hours ago, the lowest floor is submerged. Outside walls and ceilings have collapsed, the glass atrium in the lobby shattered.
"With the threat of rising seas, hotel guests have been ushered into the concrete stairwell, the sturdiest part of the building, and urged to climb to higher floors."
The massive system is causing flooding along the Louisiana coast, still recovering from Hurricane Gustav earlier this month.
1900 GALVESTON HURRICANE
Thought to be worst natural disaster in US history
8,000 people killed
130mph (209km/h) winds and 15ft (4.6m) waves swept homes away
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