"Most importantly, we give thanks to the incredible first responders, including sheriffs, police officers, firefighters, our great Cajun Navy", Trump said.
Addressing roughly 10,000 people who remain in shelters and "countless more" staying elsewhere, Cooper urged them to stay put for now, particularly those from the hardest-hit coastal counties that include Wilmington, near where Florence blew ashore on Friday.
Many areas remained cut off by floodwaters and inundated roads.
Parts of two major interstate highways were still under water Tuesday.
The storm is responsible for at least 37 deaths in the Carolinas and Virginia, officials say. The Cape Fear River was expected to crest at 61.5 feet, four times its normal height, on Wednesday in Fayetteville, a city of 200,000 near the Fort Bragg army base in the southern part of the state, according to the National Weather Service.
Flooding could begin early next week, officials said during a community meeting on Thursday, as water continues to drain into rivers and reservoirs across North and SC.
In a news conference Tuesday, Cooper warned that sunshine doesn't mean the threat is over, and rivers continue to rise.
The EPA has also said that once conditions allow, it plans are to deploy "reconnaissance teams" to inspect Superfund hazardous-waste sites in the Carolinas and Georgia.
"That rain has to go somewhere, it flows from the basin upstream down into the Cape Fear river", Amy Cannon, County Manager for Cumberland County, told McCammon. Trump is expected to visit Myrtle Beach while in SC.
As floodwaters continued to rise, concerns grew about environmental and health dangers.
As NPR reported before the storm, the waste is usually kept in large open ponds.
The flooding from Florence has also caused 21 hog "lagoons", which store manure from pig farms, to overflow in North Carolina, possibly contaminating standing water, according to the state's Department of Environmental Quality. The utility said it could not rule out the possibility that coal ash from a dump adjacent to the plant, which formerly burned coal, might be flowing into the nearby Cape Fear River.
High winds brought down trees and damaged homes.
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