In Kinston, more than an hour's drive inland from the coast, Lenoir County spokesman Bryan Hanks said a man was electrocuted as he attempted to connect extension cords outside in the rain. At least four people have died, and authorities fear the toll will go higher as the tropical storm crawls westward Saturday across SC.
The hurricane center predicts as much as 101 centimeters (40 inches) of rain for some parts of North Carolina.
Governor Cooper said there have been "several hundred" rescue operations and "there are still some people they need to get to". Dozens more were rescued from a collapsed motel.
About 1.7 million people in North Carolina, South Carolina and Virginia are under voluntary or mandatory evacuation orders, and millions of others live in areas likely to be affected by the storm.
Florence flattened trees, buckled buildings and crumpled roads. The storm knocked out power to almost 930,000 homes and businesses, and the number could keep rising.
The mother and baby were among a family of three who were in a house in Wilmington, North Carolina, when it was struck by a falling tree.
A 77-year-old in Lenoir County is believed to have died after he was blown away by heavy winds while attempting to check on his hunting dogs, Dail said. River flooding may be worse than Hurricane Floyd in 1999. "I couldn't even imagine", he said.
The storm was expected to move across parts of southeastern North Carolina and eastern SC on Friday and Saturday, then head north over the western Carolinas and central Appalachian Mountains early next week, the NHC said.
Florence had been a category three hurricane with 120mph winds as of Thursday, but dropped to a category one hurricane before coming ashore.
It is now a tropical storm but will continue to threaten North and SC with powerful winds and catastrophic freshwater flooding.
But it was clear that this was really about the water, not the wind. "It's going to be the rain".
In Jacksonville, North Carolina, city officials posted photos * a href="https://www.facebook.com/JacksonvilleNC.gov/?tn-str=k*F" target="_blank" rel="noopener" *of toppled gas pumps and a downed trees early Friday, warning residents to take shelter and avoid roadways.
"Into next week our rivers are going to continue to rise and there will be more significant flooding", Cooper said.
Authorities warned, too, of the threat of mudslides and the risk of an environmental disaster from floodwaters washing over industrial waste sites and hog farms.
Trump has been criticized for his response to Hurricane Maria, which hit Puerto Rico last September and resulted in almost 3,000 deaths.
The National Hurricane Center said Florence is expected to be re-categorised as a tropical depression by the time it moves into the mid-Atlantic states and New England in the middle of next week.
Most of those in North and SC live in Raleigh, Charlotte and Charleston. That's enough to fill the Chesapeake Bay or cover the entire state of Texas with almost 4 inches (10 centimeters) of water, he calculated.
North Carolina alone is forecast to get 9.6 trillion gallons (36 trillion liters), enough to cover the Tar Heel state to a depth of about 10 inches (25 centimeters). As they work into our area, it'll be nothing more than a good soaking of rain. Officials in the town of 30,000, which dates to the early 18th century, said over 100 people were rescued from floods and the downtown was under water by Friday afternoon.
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"The wind was so hard, the waters were so hard ..." She was eventually rescued by a boat crew; 140 more awaited assistance.
"Honestly, I grew up in Wilmington. So we made a decision to stay", she said.