The storm has taken at least one life, authorities said. Emergency management officials in Pearl River County said a falling tree struck and killed a tow truck driver who was clearing debris at midnight in Picayune, Miss., CNN reported.
The National Hurricane Center in Miami said in its 5 p.m. EDT advisory Isaac's center was about 35 miles west-northwest of Monroe, La., and about 40 miles south-southeast of El Dorado, Ark. Top sustained winds were 35 mph and the storm was moving north-northwest at 12 mph.
Isaac was expected to turn toward the north by late Thursday or early Friday. On its forecast track, the storm was expected to move out of Louisiana Thursday, into Arkansas Friday and over southern Missouri Friday night.
All coastal warning have been discontinued.
Storm surge will cause water levels to remain high in southeastern Louisiana and coastal Mississippi through Thursday night, with levels gradually receding Friday.
A storm surge of more than 5 feet was observed Thursday afternoon at New Canal Station, La. A storm surge of more than 5 feet was still present along the southern shore of Lake Pontchartrain and a surge of nearly 5 feet was occurring at Waveland, Miss.
National Weather Service meteorologist Danielle Manning said Thursday the Baton Rouge area "is out of the worst of it and is seeing the light at the end of a very short tunnel." Manning said the area will likely remain under a tropical storm warning until Isaac weakens to tropical-depression strength, probably Thursday evening, The (Baton Rouge) Advocate reported.
A flash flood watch is to remain in effect until 7 p.m. for southeast Louisiana. Officials in Ascension Parish said they were preparing for flooding from the Amite River this weekend.
Forecasters said Isaac may have spawned at least three tornadoes overnight in Gulfport and Jackson, Miss., and Geneva, Ala., CNN reported.
Mississippi and Louisiana have ordered evacuations in all low-lying areas along the Tangipahoa River, which was observed early Thursday at 17 feet -- 4 foot above flood level -- CNN said. The National Weather Service said the river was expect to rise to as high as 19.5 feet by Friday.
Residents of Washington Parish have been warned the Bogue Chitto River along the Louisiana-Mississippi line, was expected to rise by 14 feet overnight.
The office of Louisiana Gov. Bobby Jindal said a controlled release of water began during the afternoon at Lake Tangipahoa to prevent the collapse of a dam that was "badly damaged by heavy rains." Jindal said a planned controlled-breach would send water mostly into a forested area, and not into populated areas, but Tangipahoa Parish President Gordon Burgess urged mandatory evacuation as a precaution.
Jindal said Thursday thousands of people are in shelters and thousands more are under evacuation orders in Louisiana.
At least 14 people were arrested overnight in East Baton Rouge Parish for violating an overnight curfew, The (Baton Rouge) Advocate said.
In the aftermath of the storm, Olde Towne Slidell, La., was covered in thigh-deep water, and officials were conducting rescues of people trapped in their homes, The (New Orleans) Times-Picayune reported.
Sgt. Robert Crowell, a reserve officer with Slidell police, told The Times-Picayune it was unclear how many might need help, but when officers see people on porches, they ask them whether they want to be evacuated.
St. John the Baptist Parish officials said more than 3,200 people had been rescued or evacuated in neighborhoods flooded by a tidal surge from Lake Pontchartrain Wednesday, The Times-Picayune reported.
In Washington Parish, along the Mississippi state line, police went door to door to warn residents of possible flooding from the Bogue Chitto River, which was expected to rise 14 feet overnight.
Curfews were in place from New Orleans to Baton Rouge.
About 840,000 people were without power in Louisiana, Mississippi, Alabama, Arkansas and Texas.
Utility companies said power was being restored Thursday to some of the 700,000 homes and businesses affect by Isaac in southern Louisiana, the Times Picayune reported. Entergy Corp. of New Orleans said it had called about 7,000 additional line crews and contractors in to restore service in Louisiana and Mississippi and power had been restored by mid-morning to about 4,000 customers in Orleans Parish.
Rain was expected to continue to be heavy, with Isaac dropping an average 7 to 14 inches.
Isaac hit the Gulf Coast on the seventh anniversary of Hurricane Katrina, which killed more than 1,800 people in Louisiana and Mississippi.
The center of Isaac bypassed New Orleans but hit Plaquemines Parish south of the city on the flood protection system that protected New Orleans.
The locally built gulf-side levee of Plaquemines Parish was overtopped by Isaac's massive surge, deluging the area with as much as 14 feet of water, officials said.
Dozens of people had to be pulled to safety by rescue workers and neighbors. Officials went door to door early Thursday to evacuate additional people as the water crept up the west bank.