Florence's top sustained winds have weakened to 50mph (80km/h), but it is projected to bring further catastrophic flash flooding.
Some towns have already had over 2ft (60cm) of rain, and forecasters warn that totals could hit 3.5ft (1m).
Nearly a million householders have no electricity in the Carolinas.
On the other side of the world, meanwhile, more than a dozen people have died as Typhoon Mangkhut rips through the Philippines.
President Trump's disaster declaration for eight North Carolina counties frees up federal funding including grants for property repairs and low-cost loans to cover uninsured losses.
The president may travel to the region next week, the White House has said.
Five of the deaths from Florence were in North Carolina:
- A mother and her child were killed in Wilmington when a tree fell on their home on Friday. The infant's father was taken to hospital for injuries
- A 78-year-old man was electrocuted in Lenoir County while attempting to connect extension cords
- A 77-year-old man in the same county died when he was blown down by high winds while checking on his hunting dogs
- A woman died from cardiac arrest in the town of Hampstead after emergency responders had their route to her blocked by downed trees
The sixth victim - and the first in South Carolina - was a 62-year-old woman who died when her car hit a tree that had fallen across a road in the town of Union.
Two other fatalities in Carteret County were earlier blamed on the storm, but authorities later clarified a husband and wife had died in an apparent murder-suicide, reports the Charlotte Observer.
On Saturday morning, the 350-mile-wide storm was strolling along at 2mph, unleashing drenching downpours in eastern South Carolina.
About 100 people still need to be rescued in New Bern, North Carolina, where some 4,200 homes have been damaged, the mayor told CNN.
The riverfront city of 30,000 people has been deluged by 10ft of water, the National Weather Service (NWS) reported.
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