(CNN) -- More than 32 million people are under tropical storm warnings from the Gulf Coast to the mid-Atlantic Thursday morning as former Hurricane Zeta rushes northeast.

Zeta made landfall in Louisiana as a Category 2 storm Wednesday before weakening to a tropical storm, with sustained winds of 60 mph as of 5 a.m. ET Thursday.

The storm has killed at least two people and cut power to more than 2 million utility customers across the South.

As of 5 a.m. ET Thursday, Zeta's center was near the state line in northern Alabama and Georgia, about 65 miles to the west of the Metro Atlanta area lashing parts of both states with winds gusting over 70 mph.

The storm was picking up momentum -- traveling at 39 mph -- and the National Hurricane Center says an even faster northeastward movement is expected later Thursday.

"On the forecast track, the center of Zeta will move across portions of the southeastern US this morning, across the Mid-Atlantic states this afternoon, and emerge over the western Atlantic by tonight, it said Thursday morning.

Zeta to keep tropical storm intensity

Zeta's fast advance means the system won't lose much energy, CNN meteorologist Michael Guy said. This will allow Zeta to keep tropical storm intensity with strong winds throughout its course to the Atlantic.

Zeta is expected to bring strong gusty winds, isolated tornadoes and heavy rain with the potential to produce flash flooding overnight.

Hurricane and storm surge warnings have been discontinued for all of Louisiana and the Mississippi coast, but coastal areas of Alabama have been warned the storm surge threat remains due to remnant winds left in the wake of the hurricane.

At least 32.7 million people from the Gulf Coast toward the Carolinas were under Tropical Storm warnings Thusday morning. The last time metro Atlanta was under such a warning was October 2018 as Hurricane Michael passed over the region.

As Zeta moved inland across the South, it caused substantial power outages across several states. More than 2 million utility customers were in the dark in Georgia, Louisiana, Alabama, and Mississippi early Thursday, according to PowerOutage.US.

Many of the outages were in Louisiana, where the first death attributed to Zeta was reported Wednesday.

Louisiana still recovering from earlier storms

A 55-year-old man was electrocuted by a downed power line, the Louisiana governor's office, citing the Orleans Parish coroner.

New Orleans Mayor LaToya Cantrell tweeted that residents should stay home overnight.

"STAY INSIDE: Can't stress enough how dangerous the roads are right now in #NOLA. Widespread downed trees & power lines. Also, many traffic lights are out. If you MUST drive tonight, be extremely cautious & treat intersections with lights out as four-way stops. #Zeta," she wrote.

The city tweeted an image of a downed power line and warned that lines could be live.

In Mississippi, Biloxi Police Chief John Miller told CNN affiliate WLOX that a person's body was found on the Broadwater Marina, and that the death is considered storm-related.

The cause of death was not available.

Louisiana's Lafourche, St. Bernard and Terrebonne parishes issued curfews for Wednesday evening, according to authorities in each parish.

Officials in Jefferson and Terrebonne parishes had issued mandatory evacuation orders ahead of the storm for coastal areas and places outside major levees. In New Orleans, voluntary evacuations were called for similar areas.

Louisiana is still recovering from the damage caused by recent storms. About 3,600 evacuees still are displaced weeks after Hurricanes Laura and Delta caused major destruction, according to Louisiana Gov. John Bel Edwards.

Most of the evacuees have been displaced since August from Laura and have been spread among six hotels in New Orleans, the governor's office said.

Edwards said more than 1,500 National Guard members had been activated and more than 5,000 linemen are staged to begin recovery and power restoration efforts Thursday morning.

"It's going to be a rough evening for Louisiana, particular in the southeastern portion. I am confident that we are well prepared for this," Edwards said.

Alabama Gov. Kay Ivey declared a state of emergency Tuesday. On Wednesday, she asked residents to finish storm preparations quickly and warned that even the central part of the state could see tropical storm winds.

"I urge everyone to quickly finish your preparations this afternoon and stay off the roads tonight, if possible," Ivey said. "Zeta is gaining strength and will certainly give a punch to our state, and we all must be ready. Stay safe."

The National Weather Service in Mobile, Alabama, said Thursday on Facebook that it had received reports via Clarke County emergency officials of significant to major damage countywide. "Structural damage. Ambulance building destroyed. Windows blown in several homes & businesses. Numerous trees on homes & cars. Communications & internet out," it posted.

Before turning its path toward the US coast, Zeta struck the Yucatán Peninsula in Mexico on Monday night as a Category 1 hurricane.

Zeta is the 27th storm of the Atlantic hurricane season, one shy of tying the record for the most storms in a season. There were 28 storms in 2005, including 15 hurricanes.

CNN's Amara Walker contributed to this report.

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