NEW ORLEANS — City and state officials tried to hold them off, but New Orleans residents would have none of it. After Hurricane Gustav brushed by the city, they wanted back in, and now.

So Mayor Ray Nagin relented and allowed the first of them to begin streaming in from evacuation Wednesday.

But more than a million homes and businesses across three states were still without electricity and officials said it could take as long as a month to fully restore power.

As residents came home to New Orleans, President Bush returned to the site of one of the biggest failures of his presidency to show that the government had turned a corner since its bungled response to Hurricane Katrina in 2005.

Faced with traffic backups on paths into the city, Nagin gave up checking ID badges and automobile placards designed to keep residents out until early Thursday. Those who returned said if the city was safe enough for repair crews and health care workers, it was safe enough for them, too.

“People need to get home, need to get their houses straight and get back to work,” said George Johnson, who used back roads to sneak into the city. “They want to keep you out of your own property. That’s just not right.”

But once back at home, many people had no power and no idea when it might return. Outages were widespread across Louisiana and thousands more lost power in parts of Mississippi and Arkansas.

“There is no excuse for the delay. We absolutely need to quicken the pace at which power is restored,” Louisiana Gov. Bobby Jindal said.

Within hours of returning to his suburban home, Paul Braswell was sweating over an outdoor grill as he cooked the chicken and deer sausage he stored in his freezer alongside gallon-size blocks of ice before evacuating with his family to Mississippi.

“We don’t have any power, and we don’t know when it’ll come back on, so we’re going to eat all we can until it does,” he said. “Tomorrow, we’re boiling shrimp my mom left in her freezer.”

Restoring power was critical to reopening schools, businesses and neighborhoods. Without electricity, gas stations could not pump fuel and hospitals were running out of fuel for generators.

Some places never lost power, including the Superdome, where the Saints planned to open their regular football season Sunday.

In Jefferson Parish, which also reopened Wednesday, officials reported that most sewage-treatment stations were out of service because there was no power. The parish urged residents not to flush toilets, wash clothes or dishes, or even take showers out of concern that the system might backup and send sewage flowing in home and businesses.

After touring an emergency center and flooded-out farmland, President Bush praised the government response to Gustav as “excellent,” but he urged utility companies in neighboring states to send extra manpower to Louisiana if they could spare it.

“One of the key things that needs to happen is that they’ve got to get electricity up here in Louisiana,” Bush said.

The administration’s swift reaction was a significant change from its response three years ago to Katrina, a far more devastating storm. Roughly 1,600 people were killed and the White House was harshly criticized for stepping in too late.

To residents who lived through Katrina, that failure was still fresh.

“What do I care if Bush is visiting? I’m still trying to get my house back together from Katrina,” housekeeper Flora Raymond said. “This time things went better, but we still need help from the last time.”

In the days before Gustav arrived, nearly 2 million people were evacuated from the Louisiana coast. Eighteen deaths were attributed to the storm in the U.S., several of them occurring during cleanup after it had passed.

Nearly 80,000 people remained in shelters in Louisiana and surrounding states. An estimated 18,000 people fled from New Orleans on buses and trains arranged by the state and federal governments.

Nagin said Wednesday night that he hoped the process of returning the city’s evacuated residents would begin Friday and most would return by the end of the weekend, depending on weather, roads and rail conditions.

Inside the shelters, the days of living on cots with strangers on all sides was taking a toll. At a church in Montgomery, Ala., an argument in a parking lot between two sisters over the gas money needed to return to New Orleans erupted into a fight that ended with slashed tires, a punch in the face and an arrest.

“I wanted to give her something,” Samantha Williams said, holding her swelling lip. “But she wanted so much more.”

Five people were arrested Wednesday in only the second case of attempted looting in New Orleans since the city emptied. Worried about potential looting of vacant properties, Nagin said the city would maintain its dusk-to-dawn curfew indefinitely.

There were fresh reminders that the 2008 hurricane season is far from over. Tropical Storm Hanna pounded flood-plagued Haiti before taking an expected turn north for the U.S. coast. Farther out to sea, Hurricane Ike reached Category 4 strength as it spun westward across the Atlantic and could arrive in the Bahamas on Sunday.

Tropical Storm Josephine was out there, too.