The center of Barry will move across the western and northern portions of Louisiana on Sunday and over Arkansas on Sunday night and Monday, the NHC said.
With maximum sustained winds of 40 miles per hour, Barry was moving north at 9 miles per hour, the National Hurricane Center said in its 10 a.m. CDT advisory.
The heat and humidity will continue Tuesday as remnants from Tropical Storm Barry start to roll through Northeast Ohio.
But it said "life-threatening storm surge inundation" continued as it moved inland.
Edwards said the state and levees in New Orleans were ready for impact and should withstand the floodwaters.
All flights in and out of the airport in the state's biggest city New Orleans were cancelled, thousands had evacuated their homes, tens of thousands had lost power and first responders were poised for action. "It's going to be a long several days for our state". Areas along the path of the storm near the MS and lower OH valleys where they are susceptible to torrential rains, flash flooding, and even a few twisters.
At the Pac Shack restaurant, owner Amanda Ekiss said the water was over 10 feet high this weekend.
The sunny weather is expected to last until about 2 p.m., with the potential for rain until around 3 p.m., the National Weather Service said on its website.
Louisiana Gov. John Bel Edwards said Sunday he was "extremely grateful" that the rain and flooding wasn't as severe as forecast and that "the worst-case scenario did not happen".
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Heavy rain is expected throughout the state.
Forecasters said up to 14 inches (36 centimeters) of rain had already fallen some spots in southwest Louisiana.
Even as a weaker tropical depression Monday, Barry is still dumping heavy rain on parts of Louisiana, Mississippi and Arkansas, prompting a wave of new flash flood watches.
Over the next hour and a half, the water rose another foot and the wind kept on getting stronger. The highest risk of severe weather on Monday will be over MS, but there is also a low-end chance that s storm becomes severe over Alabama too. Mandatory evacuations were ordered for all areas along Louisiana Highway 315. Part of the main road was flooded Saturday afternoon, as were some waterfront businesses, with water rising by the minute.
Ludovico Torri woke up Saturday morning to a surprising sight: Lake Pontchartrain was at the door of his Mandeville home, just north of New Orleans.
"Based on what we've experienced, I think (we will be) even better prepared for next time - and we do know that there will be a next time", Edwards said.
The location of the center of the system is not important at this point.
The rain was expected to raise the already flooded Mississippi River but not overtop the levees.
Contributing to this report were Associated Press writers Kevin McGill and Rebecca Santana in New Orleans; Jay Reeves in Baton Rouge; Juan Lozano in Lafayette; Rogelio Solis in Morgan City; and Jeff Martin in Atlanta.
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