Residents (from left) Mike Haddock, 48, Katlyn Humphrey, 19, Michelle Haddock, 45, and Justin Humphrey, 24, remove possessions from the Haddock's flooded home using a jon boat in Trenton, North Carolina.
One person was killed in Virginia when the storm spawned some 16 tornadoes there on Monday, according to the National Weather Service.
Officials have identified the two mental health patients who drowned when a van they were riding in was swept away in SC flood waters.
The death toll from Hurricane Florence had increased to 32 people on Tuesday morning, as officials rushed to get relief to a North Carolina city still largely marooned from the rest of the state by flood water.
Cooper warned that the flooding set off by the Southeastern deluge was far from over and will get worse in places.
The White House said President Donald Trump will visit North Carolina on Wednesday to see the damage.
Trump's trip to the state follows criticism for his handling of Hurricane Maria, which devastated Puerto Rico past year, and more recently for disputing the official death toll of 3,000 in the USA territory.
The water level of the Cape Fear River was expected to crest at 61.8 feet by Tuesday.
Tens of thousands of homes have been damaged. That has hampered efforts to restore power, clear roads and allow residents to homes.More news: Trump says Federal Bureau of Investigation should not probe allegations against top court pick
Flooded vehicles sit on a closed section of Interstate 95 in Lumberton, North Carolina, where the Lumber River overflowed following flooding from Hurricane Florence.
"The Company estimates that approximately 1.7 million head of broiler chickens out of an average live inventory of approximately 20 million head, ranging in age from six days to sixty-two days, were destroyed as a result of flooding", Sanderson Farms said in a statement this week.
"I think the next 48 hours are going to be incredibly critical", he said.
Property damage from the storm is expected to range from $17 billion to $22 billion, the risk management firm Moody's Analytics said.
In South Carolina, 40 major roads were closed.
Preliminary statistics from the National Oceanic and Atmospheric Administration showed Florence had the fourth-highest rainfall total of any hurricane to hit the US mainland since 1950, with 35.94 inches (91.2 centimeters) at Elizabethtown, North Carolina.
"I know for many people this feels like a nightmare that just won't end", he said.
After submerging North Carolina with almost 3 feet (1 meter) of rain, the storm dumped more than 6.5 inches (16.5 centimeters) of rain in the Northeast, where it caused flash flooding, wind damage and prompted at least one tornado warning, the weather service said.