More than 1 million people, mainly in North Carolina, were without power a day after Florence made landfall a few miles east of Wilmington as a howling Category 1 hurricane.
The tree was about 6 feet above the road surface.
Cooper warned against such behaviour as roads become increasingly risky.
"Life-threatening, catastrophic flash floods and prolonged significant river flooding are likely over portions of the Carolinas and the southern to central Appalachians from western North Carolina into west-central Virginia through early next week, as Florence moves slowly inland", the NHC statement read. The great danger now, experts say, is river flooding. "More and more inland counties are issuing mandatory evacuations to get people to safety quickly".
Florence crashed ashore Friday morning in North Carolina as a Category 1 hurricane, and it has wiped out power to about 796,000 customers in that state and SC, reports CNN.
In the town of New Bern, homes were completely surrounded by water, and rescuers had to use inflatable boats to reach people.
None of the people rescued were injured. "We still have about 100 that want to be rescued and we have about 1,200 in the shelters", Mayor Dana Outlaw told CNN.
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Over 895,000 without power as Florence batters Carolinas
When Hurricane Florence made landfall in North Caroline, Weather Channel reporter Mike Seidel was out in the storm reporting live. Officials said some 1.7 million people in the Carolinas and Virginia were warned to evacuate, but it was unclear how many did.
In its initial onslaught along the coast, Florence buckled buildings, deluged entire communities and knocked out power to more than 870,000 homes and businesses.
Glover speculated that part of the problem could stem from an "until I can get to higher ground and make sure my family is safe, I can't talk to media", mindset. "We can pump 42,000 gallons (159,000 litres) a minute once we have water receded enough".
The Coast Guard is working to rescue people trapped in the northeast part of North Carolina, and reported rescuing five individuals so far.
A 61-year-old woman was killed late Friday when the vehicle she was driving struck a tree that had fallen across Highway 18 near the town of Union. "I love hurricanes. But this one has been an experience for me", she said.
Tropical Storm Florence dumped "epic" amounts of rain on North and SC as it trudged inland on Saturday, triggering risky flooding, toppling trees, cutting power to almost a million homes and businesses while causing at least five deaths.
The storm has now shaped up as a two-part disaster, with the second, delayed stage triggered by rainwater working its way into rivers and streams.
Most of the fatalities occurred in North Carolina, where officials confirmed eight victims.
In total, Florence is forecast to dump about18 trillion gallons of rain over North Carolina, South Carolina, Virginia, Georgia, Tennessee, Kentucky, and Maryland before the storm is over.
North Carolina's Republican-controlled legislature enacted House Bill 819 (pdf) in 2012, after the state's Coastal Resource Commission published a 2010 report (pdf) predicting that seawater could rise 39 inches along the coast by 2100, and lawmakers, coastal landowners, and members of the real-estate industry responded with alarm over pricey waterfront property that could face billions of dollars in damage.
SC authorities said law enforcement officers were guarding against looting in evacuated areas, while Wilmington set a curfew on Saturday evening in response to looting in one area.