Some low-lying areas of Houston remain flooded
A week-long curfew has been imposed in Houston to prevent looting in the wake of Hurricane Ike which hit the US city and many other parts of Texas.
The night-time curfew is needed because most of America's fourth-largest city is without power, officials say.
Meanwhile, rescuers have evacuated nearly 2,000 people from the worst hit areas along the Texan coast.
Texan oil refineries put out of action by the storm could take up to nine days to recover, a US official has warned.
Hurricane Ike made landfall in Galveston, Texas, early on Saturday with 110mph (175km/h) winds.
It cut a 500-mile (800-km) swathe of destruction across a span of the Gulf of Mexico coast before weakening to a tropical depression over Arkansas on Sunday.
Ike has so far been blamed for eight deaths - five in Texas, two in Louisiana and one in Arkansas.
The authorities in Houston said the 2100-0600 curfew was imposed because downed power lines had cut electricity to millions of people.
"Transportation arteries are still very very dangerous. Power's out and there are no street lights, there's still limbs down, there's still standing in water," said Judge Ed Emmert of Harris County, which includes Houston.
"Please don't venture out unless you absolutely have to," Judge Emmert urged residents.
Officials also said that city schools and regional airports would remain closed for some time.
The authorities estimate that up to 140,000 Texans ignored the mandatory orders to flee ahead of the storm.
In the coastal city of Galveston, which bore the brunt of the hurricane, relief workers have been using boats, high-wheel trucks, and helicopters to undertake a door-by-door search through flooded streets and damaged buildings.
On Sunday Texan authorities said 1,984 people who had refused to evacuate had been rescued so far, including 394 by air.
President George W Bush - who is due to visit Texas on Tuesday - urged residents who had obeyed evacuation orders ahead of the storm to also follow warnings from local authorities before trying to return to the affected areas.
Meanwhile, 600 people were rescued in neighbouring Louisiana, where flooding ruined tens of thousands of homes and left nearly 200,000 householders without electricity.
In a separate development, Texan Senator Kay Bailey Hutchison said power outages and flooding at the state's oil refineries meant refined gasoline was "going to be in a shortage situation".
In an interview with CBS, Sen Hutchison said she had been told by officials at the Federal Emergency Management Agency (Fema) that the facilities were "pretty much down".
"We are looking at another week or eight or nine days before refineries are up and going, so refined gasoline is going to be in a shortage situation because of the power outages and flooding," she said.
"It is going to be felt for the next week that we have gasoline shortages, so people need to be prepared for that."
Earlier, the oil company, Chevron, said it was "concerned about severe gasoline supply disruptions in the wake of Hurricane Ike".
Production was halted at 15 oil refineries in Texas, including the giant Exxon Mobil refinery in Baytown, ahead of the storm. Together, they make up just under a quarter of US fuel production capacity.
The storm also shut down crude oil production in the Gulf of Mexico, which is responsible for a quarter of total US output.
Ike sent fuel prices higher at the pumps and, analysts say, has triggered the biggest disruption to US energy supplies in at least three years.