Mother Lesha Murphy-Johnson and her baby, Zac, were killed after being trapped inside their home in Wilmington when a tree fell onto the roof at around 9.30am on Friday.
Police confirmed the fatalities on Twitter, saying the father of the child was being transported to a local medical centre to be treated for his injuries.
The NWS says southern and central portions of North Carolina into far northeast SC are expected to report an additional 10 to 15 inches of rainfall - with storm totals between 30 and 40 inches along the coastal areas south of Cape Hatteras.
"The fact is this storm is deadly and we know we are days away from an ending", Cooper said.
Atlantic Beach on North Carolina's Outer Banks islands had already received 30 inches (76 cm) of rain, the U.S. Geological Survey said.
The hurricane center predicts as much as 101 centimeters (40 inches) of rain for some parts of North Carolina.
More than 1.7 million people evacuated this week, leaving behind homes, schools and precious belongings.
The total extent of devastation from Florence, which has turned from a hurricane into a tropical storm, remains unknown as rain and flooding continue to wreak havoc in the Carolinas.
A 78-year-old man in Kinston, North Carolina, was electrocuted when he tried to connect two extension cords outside in the rain, according to Lenoir County Emergency Services Director Roger Dail.More news: NHC says Florence has weakened to a tropical storm
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"It will not stop, this weather event of Florence", Begnaud said.
Winds bent trees towards the ground and raindrops flew sideways as Florence moved in for an extended stay, with enough of its killer winds swirling overseas to maintain its power. The center of the hurricane´s eye came ashore at about 7:15 a. m. EDT (1115 GMT) near Wrightsville Beach close to Wilmington, with sustained winds of 90 miles per hour (150 kph), the National Hurricane Center (NHC) said.
The flooding soon spread into SC.
Florence was a Category 3 hurricane on the five-step Saffir-Simpson scale with 120-mph winds on Thursday.
View of Florence in Wilmington, N.C., on Friday.
In New Bern, a city that backs on to the Neuse river in North Carolina, rescue operations continued on Saturday as significant flooding destroyed homes and some of the city's historic colonial-era statues.
Still, he said: "I feel like the dumbest human being who ever walked the face of the earth". "For overall damage, it would be hard, at the end of the day, I think, to find a rival for this storm". "We got thrown into mailboxes, houses, trees", said Holt, who had stayed at home because of a doctor's appointment that was later cancelled. Unsafe storm surge could also affect portions of the northeast coast of South Carolina Saturday.
For people living inland in the Carolinas, however, the moment of maximum peril from flash flooding could arrive days later, because it takes time for rainwater to drain into rivers and for those streams to crest.
Before dawn on Friday, authorities had been forced to rescue more than 60 people in Wilmington, some who had ignored evacuation orders.
Tropical Storm Florence is continuing to dump unsafe amounts of rain as it continues its slow slog across the Carolinas.