The storm had New Orleans in the center of its path, nearly seven years to the day after the city was devastated by Hurricane Katrina.
Governors of Louisiana, Alabama and Mississippi declared states of emergency and tens of thousands of people were ordered to evacuate.
Authorities said Florida had avoided the worst of Isaac but was still feeling its effects. The Republican National Committee pushed back the first day of the party's convention in Tampa from Monday to Tuesday.
The National Hurricane Center declared a hurricane warning for an area stretching from east of Morgan City, La., to Destin, Fla. That arc includes New Orleans, Lake Pontchartrain and Lake Maurepas.
The hurricane center said in its 8 p.m. EDT advisory Isaac had beefed up and slowed down, with sustained winds hitting 70 mph, and was expected to become a hurricane "soon" -- sometime Monday night or early Tuesday.
Isaac was centered about 230 miles southeast of the mouth of the Mississippi River and about 295 miles south-southeast of Mobile, Ala., moving to the northwest at 10 mph.
The hurricane center said the center of Isaac was moving over the eastern Gulf of Mexico and would approach the northern Gulf Coast Tuesday, by which time the storm could be a Category 2 hurricane with winds reaching 96 to 110 mph, Accuweather.com reported.
Tropical storm-force winds extend 205 miles out from the center of the storm and the storm surge could reach as high as 12 feet along the gulf coast, the hurricane center said.
The (New Orleans) Times-Picayune reported Louisiana Gov. Bobby Jindal had activated 4,126 Louisiana Army and Air National Guard troops in anticipation of the storm's impact.
Jindal said the troops were helping set up evacuation shelters and also would serve as bus drivers.
The newspaper said military officials said the Coast Guard had abandoned its boat stations in Grand Isle and Venice, and Coast Guard and Navy aircraft were being moved from the New Orleans metro area to Houston.
USA Today reported federal authorities said high water from up to 18 inches of predicted rain, not Isaac's gales, constituted the primary concern. The newspaper said people in the target zone were buying food, water and gasoline in anticipation of the storm's arrival.
"I gassed up -- truck and generator," John Corll, 59, a carpenter in New Orleans who lived through Katrina, told USA Today. "I think the state and local governments are much better prepared for the storm surge and emergencies."
Billy Cannon, 72, of Gulf Shores, Ala., said he thought the evacuation was premature.
"If it comes in, it's just going to be a big rainstorm," he said. "I think they overreacted, but I understand where they're coming from. It's safety."
Airlines were expected to cancel scores of flights Monday and even more in the coming days. Amtrak canceled train service into Louisiana for Tuesday and Wednesday.
Craig Fugate, director of the Federal Emergency Management Agency, expressed concern Monday people in the entire projected impact zone might linger too long.
"We need people to go now," he said.
"This is not a New Orleans storm. This is a Gulf Coast storm."
Jindal ordered 53,000 residents of St. Charles Parish near New Orleans to get to safe ground.
"Hope for the best as you prepare for the worst," Jindal said in Baton Rouge.
CNN reported Alabama Gov. Robert Bentley ordered mandatory evacuations for residents along the coast and those in some low-lying areas inland.
"I am urging everyone to take precautions now," he said.
Mississippi officials dispatched 1,500 National Guard troops and distributed 10,000 sandbags to residents ahead of the storm.
"In short, we have done everything in our power to be prepared for the storm," Mississippi Gov. Phil Bryant said.
More than 18,000 residents in Miami-Dade, Broward and Palm Beach counties on the state's east coast were without power Sunday night, The Miami Herald reported.
Hundreds of flights were canceled at South Florida airports.
Along Florida's west coast, emergency shelters opened in Pinellas and Hillsborough counties surrounding Tampa Bay, the Tampa Bay Times reported.
The storm was predicted to drop 2 to 4 inches of rain in the Tampa Bay area by Monday night, but Florida Gov. Rick Scott said he was most concerned about how it might affect northern sections of the state, which were still waterlogged from Tropical Storm Debby.
Wednesday is the seventh anniversary of Hurricane Katrina, which struck the Gulf Coast with 145 mph winds, devastating a region that included New Orleans.
More than 1,700 people were killed and hundreds of thousands of others were displaced by Katrina, which was a Category 3 hurricane. Its storm surge -- a 29-foot wall of water -- was the highest ever measured in the United States.