Evacuation orders, most voluntary, were in effect in several Louisiana parishes as officials confront threats of flooding from rain-swollen waterways, CNN reported.
In St. Tammany Parish, north of Lake Ponchartrain, officials warned residents not to return while authorities worked to relieve pressure created by a weakened lock on a canal.
"As there is still a potential threat, even though reduced, a voluntary evacuation remains in place until the Army Corps of Engineers deems the lock stable and safe," Pat Brister, president of St. Tammany Parish, said Sunday. "Please stay vigilant."
Forecasters said the Pearl River should crest Monday at 19.5 feet, at least 5 feet above flood stage, potentially threatening several thousand homes in St. Tammany, CNN said.
President Obama was to visit the state Monday afternoon.
When it made landfall, Isaac it was much weaker than Hurricane Katrina, which killed nearly 1,800 people in 2005. But Isaac moved more slowly than Katrina and dumped huge amounts of rain on Louisiana and Mississippi.
In Mississippi, a flood warning was issued north of Gulfport because of the waterlogged Wolf River, expected to crest Tuesday more than 8 feet about flood stage, CNN said.
More than 3,500 people were in shelters across the state as of Sunday, Louisiana Gov. Bobby Jindal's office said.
In Mississippi, about 100 people remained in shelters, state officials said.
Feederal housing inspectors were in New Orleans, checking for structural damage caused by Isaac.
Officials said more than 400 inspections by Federal Emergency Management Agency inspectors had been conducted since Isaac made landfall, and more were scheduled as residents report their uninsured or underinsured losses, The (New Orleans) Times-Picayune reported.
"The housing inspections are an essential part of the recovery process for survivors who need to make their homes livable again or have serious personal property loss," federal coordinating officer Mike Hall said.