But under pressure from evacuees, New Orleans Mayor C. Ray Nagin (D) announced late Tuesday that all residents of the city would be allowed to come back after 12:01 a.m. Thursday.

While the worst was avoided — there were no major levee breaks of the sort that inundated New Orleans after Hurricane Katrina in 2005 — Louisiana Gov. Bobby Jindal (R) cautioned that the state still faces major hurdles before life returns to normal.

“This was a serious storm that has caused major damage,” Jindal said, as the hurricane’s trailing edge continued to dump rain across the state. “This is a challenge that is not going away overnight. We did not have the levee breeches, but we have major challenges from Hurricane Gustav.”

Extensive power outages were among the most immediate problems, with some towns completely without electricity. More than 130 transmission lines and dozens of substations were knocked out of service, meaning Gustav was surpassed only by Hurricanes Katrina and Rita in 2005 in the destruction caused to the region’s electric grid.

About 1.4 million customers were without power in Louisiana, and vast portions of the New Orleans and Baton Rouge areas have been knocked off the national electricity grid, said Kevin M. Kolevar, assistant secretary of energy for electricity delivery and energy reliability.

Of immediate concern were about a dozen hospitals that had limited electricity service, raising the possibility that some of the 800 patients will need to be evacuated — in addition to the hundreds already removed to more secure facilities, Jindal said.

State and federal officials said they were moving fuel to hospitals and other key facilities to ensure that they can continue to run generators.

To clear debris, distribute supplies and secure communities isolated by the storm, thousands of National Guard troops, federal law enforcement officers and other emergency workers were being deployed.

Meanwhile, Gustav continued to spawn bad weather. The National Weather Service reported that a tornado touched down in New Orleans’s West Bank neighborhood Tuesday night, and there were reports of flooding along several rivers in residential neighborhoods on the northern shore of Lake Pontchartrain, roughly 20 miles north of New Orleans.

There had been concerns that the storm would disrupt energy supplies from the Gulf of Mexico, which accounts for 25 percent of U.S. oil and 12 percent of natural gas production. But Energy Secretary Samuel W. Bodman said initial flights showed no visible damage to 3,842 oil and gas platforms along the coast, and he expected quick restoration of production.

“At this point we believe there’s little damage that has been caused, and within two weeks we can see us approach that 100 percent production level,” Bodman said, adding that authorities saw no signs that rigs were set adrift, dragging anchors that could damage pipelines on the sea bed, as occurred in Hurricane Katrina.