Wilmington, North Carolina police said the mother and her infant were killed after a tree fell on their house.
The father was taken to hospital, reportedly in a critical condition.
Hurricane Florence made landfall near Wrightsville Beach, N.C., at 7:15 a.m. ET, creeping slowly ashore - but bringing strong winds, a massive storm surge and a rain system that will soak much of the state and SC for days.
"Experts claim that this is just beginning of this catastrophe".
Officials in New Bern, which dates to the early 18th century, said over 100 people were rescued from floods and the downtown was under water by Friday afternoon. "We are stuck in the attic". The video shows The Weather Channel's Mike Seidel reporting from Wilmington in North Carolina, USA, reports AJC. "It's going to be more costly to a family with a baby who has to provide formula and diapers or a home that has someone with a medical issue". "It's something we haven't seen. ever".
More than 3,000 inmates at North Carolina prisons and juvenile detention centers were moved out of the storm's path.
Florence was downgraded to a Category 1 hurricane on Thursday evening with peak winds of 90 miles per hour (150 km/h).
Onslow County spokesman Cornelius Jordan said some visitors at the Triangle Motor Inn were able to drive away on their own, but emergency personnel had to take others to a safe location.
Hurricane Florence has caused some damage to Wilmington International Airport, said Gary Broughton, the airport's deputy director.
Power outages increased throughout Friday.
Dozens of North Carolina residents, as well as least nine animals, were rescued Friday night into early Saturday morning in the state's third-largest county, Cateret, according to a county EMS spokesperson.
Storm surges could reach 11 feet Saturday along coastal areas, particularly between Cape Fear and Cape Hatteras.
As of 8 p.m., Florence was centered about 85 miles (135 kilometers) southeast of Wilmington, its forward movement slowed to 5 mph (7 kph).More news: Manchester City's Pep Guardiola reveals Barcelona return plans
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Two people died in Lenoir County. "We know our customers share our commitment to the communities we serve, and together, we will continue to support the American Red Cross' disaster recovery efforts".
"Into next week our rivers are going to continue to rise and there will be more significant flooding", Cooper said.
Cooper said Florence was set to cover nearly all of North Carolina in several feet of water.
Storm surges - the bulge of ocean water pushed ashore by the hurricane - were as high as 10 feet (3 meters).
South Carolina Department of Transportation head Christy Hall said trees are already down in areas of Horry County and citizens should prepare for flooding.
Emergency crews were stretched thin.
About 9,700 National Guard troops and civilians were deployed with high-water vehicles, helicopters and boats.
The danger came in the form of a massive storm surge.
Travel on the state's roads has grown "extremely hazardous", said Jim Trogdon, the North Carolina transportation secretary, who warned in a late-morning briefing that a 500- to 1,000-year "flood event is anticipated".
Thousands of people hunkered down in schools, shelters and a coliseum in Winston-Salem.
The storm's movement, not its strength, has forecasters and officials anxious.
Tom Ballance said his wife went to Atlanta and he stayed behind in their New Bern home with their three dogs and a cat. The Neuse River rose rapidly, overcoming the streets of New Bern.
Craven County Emergency Management confirmed reports there are New Bern residents trapped on rooftops. Additional swiftwater rescue teams were on the way. In New Bern, the unsafe conditions prompted officials in the coastal city to place the city under 24-hour curfew at 7 a.m. Friday.