An elevated risk of landslides is now expected in western North Carolina.
Forecasters say prolonged rainfall from Florence could produce catastrophic flash flooding and significant river flooding.
Deadly storm Florence drenched North Carolina with more downpours on Sunday, cutting off the city of Wilmington, damaging tens of thousands of homes and threatening worse flooding as rivers fill to bursting point.
Even though Florence was downgraded to a tropical storm after it made landfall, it is proving to still be unsafe.
The tree was about 6 feet above the road surface.
Cooper said others should not follow suit. "People that are evacuating are wanting to come back (soon) and they're disregarding the flood impact, and there's going to be no power, no food".
"This system is unloading an epic amount of rainfall: in some places, measured in feet, not inches".
The Swansboro total of 86.08 centimetres is the most for any tropical storm or hurricane north of Florida along the East Coast and represents a new two-day and three-day rainfall record for North Carolina.
Members of the military, volunteer groups and first responders used boats and helicopters to rescue hundreds of people stranded in cars and homes. "That's why we've been preaching to people that you have to get away from the water".
"We have 4,200 damaged homes", he said, urging residents to not wade out into the streets because of the dangers posed by downed power lines.
Roads became flooded, trees blown over and homes destroyed as some parts of North Carolina have already seen surges of flood water as high as 10ft. She added that the department, after assessing the damage, will "hold the utility accountable for implementing the solution that ensures the protection of public health and the environment".
Governor Cooper has cautioned people in affected areas against leaving safe shelters to return home to inspect damage to their homes.
At least 10 people have died so far in the storm in North Carolina, including a mother and child killed by a falling tree, state officials said.
Firefighters said the area had not been in the zone under evacuation orders.
South Carolina Governor Henry McMaster on Saturday announced the death of a 61-year-old woman who died when her auto hit a downed tree on a highway. A 78-year-old man was killed while trying to connect extension cords outside in the rain, ABC News reported, citing Lenoir County Emergency Services Director Roger Dail.
Roger Hedgpeth, carrying his dog Bodie, gets help getting to higher ground via the United States Coast Guard during Tropical Storm Florence in Lumberton, North Carolina, U.S. September 16, 2018.
Radar showed parts of the sprawling storm over six states, but North and SC were in the bull's-eye.
The army previously announced it was deploying almost 200 soldiers to assist in storm response and recovery efforts, along with 100 trucks and equipment.
The storm known as Florence has created a slow-motion natural disaster for the Carolinas that could prove deceptively lethal as swollen rivers and streams spill over their banks and continue to rise.
In North Carolina, more than 900 people were rescued from rising flood waters and 15,000 remained in shelters, North Carolina Governor Roy Cooper told a news conference on Sunday.
After looking at an analysis of expected rainfall, flooding and the effects of Hurricane Matthew, which hit SC as a Category 1 storm in 2016, officials determined that the Pee Dee River basin could flood, swelling rivers that would overtake a number of bridges on major routes, as early as Monday night.