The storm shattered the windows of skyscrapers, showering streets with glass and debris, tore apart bus shelters and ripped metal sheets off buildings.
According to an early computer-model estimate of damage by the insurance industry, it could lead to between $8bn and $18bn in claims.
Hurricane Ike weakened to a tropical storm on Sunday, and was now heading north towards Canada where it was expected to bring heavy rains.
Michael Chertoff, homeland security secretary, said at least 940 people had been rescued so far in Texas, but there were still fears that there may have been some storm-related deaths.
"We obviously are concerned," Chertoff said in Austin, the state capital. "There may be people we find who did not get out and be in the rubble."
Chertoff planned to tour the storm-battered region on Sunday.
Officials on Sunday urged the two million people who left their homes before Ike struck to stay away for now.
"We do not want people to come back permanently," David Smith, mayor of Friendswood in Galveston County, Texas, said.
"Resources are stretched. There is no power now."
In Galveston, where the storm came ashore, boats were tossed out of the water and thrown onto the main highway with other wreckage, making it impassable.
But the vital Houston Ship Channel was not hit as hard as expected by a storm surge that could have caused far greater damage and swamped refineries.
"Fortunately the worst-case scenario that was spoken about, that was projected in some areas, did not occur," Rick Perry, Texas governor, said.
However, "very heavy damage" did occur to the power grid, he said. As a result, at least 4.5 million people could face weeks of power outages.
|Search and rescue missions are under way across areas of Texas [AFP]
In Beaumont, Texas, authorities said the damage was so extensive that it could be more than a month before power is restored and residents choosing to stay in the area must be prepared to be self-sufficient for weeks.
The storm hit Galveston as a Category Two hurricane, flooding the island city with sea water at least three metres deep in some areas and causing extensive damage.
The first aerial pictures showed homes surrounded by water and Steve LeBlanc, Galveston city manager, said 17 buildings had collapsed.
More than half the city's 60,000 residents fled before the storm.
Bobby Jindal, Louisiana governor, said more than 3,000 National Guardsmen were in hard-hit areas along the coast, helping residents to high ground and more than 200 people have been rescued so far.Energy disruptions
Ike triggered the biggest disruption to US energy supplies in at least three years and increased the price of petrol.
Oil traders will have a chance to react during an electronic trading session on Sunday.
Eight of the 14 Texas oil refineries shut down before Hurricane Ike could cause serious damage or flooding, and refineries along the western shore of Galveston Bay and Port Arthur may have been spared the worst of the flooding, according to local officials.
Ken Kalthoff, an NBC reporter in Houston, Texas told Al Jazeera: "There is a lot of damage in Houston, it is not leveling devastation but there are many problems.
"Without electricity in such a huge area ... there are big problems with getting gasoline ... there are long lines in places where there ice is being handed out.
"Police are out in force to keep things secure," he said.
Ike comes in the midst of a heavy storm season in the US and Caribbean and just 10 days after hurricane Gustav struck the US coast.
The hurricane has already battered the Caribbean, causing at least four deaths in Cuba, where about 2.6 million people were evacuated, and thousands of buildings and crops damaged.