NEW ORLEANS — Nearly a week after Hurricane Ida slammed into the Gulf Coast, leaving behind extensive power outages and escalating despair, this city began evacuating some residents in an effort to give them a respite from the punishing heat.

Authorities said the evacuations, which began Friday, are voluntary and aimed at helping the city’s most vulnerable. On the same day, utility officials laid out a timeline for returning power to storm-battered areas, including across greater New Orleans by the middle of next week.

“Even as power is being restored, and we’re seeing steps towards that, we do recognize that not everyone has it,” New Orleans Mayor LaToya Cantrell said Friday afternoon. “The stressors are remaining.”

Ida’s fallout continues to reverberate across various regions of the country, leaving people scrambling for essentials like groceries and fuel. In the Northeast, where Ida’s remnants unleashed devastating rains and killed dozens of people across four states, elected leaders said that they expected the death toll to rise and would review how officials prepared. In Louisiana, President Biden toured the devastated areas on Friday and acknowledged the frustration residents felt waiting for power to return.

Hours-long gas lines have stretched through the area, as people seek fuel for their cars and generators. The search for fuel sent some from Louisiana over the state line into Mississippi, to places like Picayune and Poplarville, where the power was on and gas was flowing. At a Love’s Travel Stop in Poplarville, people were parked at the pumps with truck beds full of dozens of gas cans — filling them to take back to greater New Orleans.

Entergy, the largest utility in Louisiana, on Friday released estimates for when power could return to storm-battered areas, saying that more lights could begin flickering on over the next several days, including as soon as Saturday in the city’s central business district. Under these estimates, power could be on across greater New Orleans by next Wednesday — 10 days after Ida hit.

“They say it’s coming back up here by Monday maybe, but who knows if you can trust that,” said Trina Williams, who sat outside the Lyons Recreation Center in Uptown New Orleans on Friday drinking a bottle of water.

Scores of people gathered outside the center on Friday to grab free meals and water. Some took seats inside parked city buses that served as mobile cooling centers.

Williams said she was staying in town. She didn’t have enough fuel to make it out of town, and she’d heard that hotels were booked everywhere you looked from west to east.

“Just going to ride it out,” she said. “At least there’s an end in sight, maybe.”

In parts of New Orleans, numerous streets were still blocked, as dozens of workers sought to untangle power lines from downed trees and raise fresh electrical poles — replacing equipment that was snapped by Ida’s winds.

The utility company warned that it might take longer for power to come back in certain cases, and pledged to “continue working until every community is restored.” Entergy Mississippi, meanwhile, said it expected most customers impacted by Ida and then a midweek rainstorm to have power back by Friday night.

Cantrell, the New Orleans mayor, said the evacuations began Friday with special-needs residents, seniors and other vulnerable people who wanted to leave the city until power returns and head to state-run shelters elsewhere in Louisiana and places including Texas.

“I am cautiously optimistic that the timeline that has been provided by Entergy will be complete by those deadlines, but . . . I am expecting more sooner rather than later,” she said.

Beginning Saturday, she said, the rest of the New Orleans population could begin evacuating on the buses. Collin Arnold, director of the New Orleans Office of Homeland Security and Emergency Preparedness, said the evacuations were primarily aimed at “the people that really are vulnerable to heat and really need this,” asking others leave space for people who “might need it more.”

Elsewhere in Louisiana, officials said they were still investigating the deaths of vulnerable residents in the state — three nursing home residents who died after being evacuated.

The Louisiana Department of Health on Thursday said the coroner had deemed these deaths “storm-related.” A fourth nursing-home resident died, but officials did not connect that to the storm.

They were among hundreds evacuated to a facility in Independence, located in Tangipahoa Parish, the department said. A spokesman later described the facility as a warehouse. The health department said it had launched an investigation and that its inspectors were repelled earlier this week after hearing about poor conditions and trying to examine it.

Officials have not said how they linked the deaths to the storm or explained how the people died. The Tangipahoa Parish Coroner’s Office did not answer questions Friday about the deaths, writing in an email: “This case is under investigation.” The sheriff’s office and police chief did not respond to messages, and the Louisiana State Police said that its investigators were in Independence and declined further comment.

Jeff Landry, the Louisiana attorney general, said Friday his office had launched an investigation into the case, saying its aim was “to determine who decided to move these patients to this apparently unsafe and potentially inappropriate facility.”

All seven nursing homes that evacuated residents to the facility in Independence are owned by Bob Dean. Several attempts to reach Dean on Friday at phone numbers associated with him were unsuccessful.

Relatives questioned the decision to move the residents from these facilities to a warehouse.

“We were under the understanding they were going to be evacuated to another nursing facility,” said Renetta DeRosia, 55, whose mother, Loretta Duet, was in the warehouse. She only learned otherwise when a friend called about the warehouse being in the news.

DeRosia went to the nursing home last week to help her mother pack, and said some residents seemed to be looking forward to evacuating — excited about a change of scenery after months of coronavirus lockdowns and the home’s strict social distancing protocols.

“It’s horrible,” DeRosia said of what happened.

Sabrina Cox, 50, said her aunt, 88-year-old Bonnie Correnti, was also at the Independence facility. Family members struggled to find her after she was evacuated, eventually locating her on a military base, Cox said.

“I don’t trust anything,” Cox said. “I want to physically see her. As soon as I get a physical address, I’m going to go up there and check on her myself.”

Berman reported from Washington. Alice Crites and Maria Paul in Washington contributed to this report.