The coastal city of Wilmington, North Carolina, has been completely cut off from the rest of the state because of deepening flood waters.
Officials say all roads in and out are now impassable and have warned evacuated residents to stay away.
Reports describe the city, which has a population of about 120 000, as an island within the state.
About 400 people there have been rescued from flood waters, and most of the city remains without power.
The National Weather Service has warned of at least two further days of possible flash flooding in the area before conditions are forecast to improve.
“Do not come here,” New Hanover County Commission Chairman Woody White said.
“Our roads are flooded, there is no access into Wilmington…We want you home, but you can’t come yet.”
Two of the first known fatalities – that of a mother and her seven-month son – were reported in the city on Friday morning.
The area is usually best known as a filming location for US dramas One Tree Hill and Dawson’s Creek.
US basketball legend Michael Jordan – who is fundraising to help residents affected by the storm – also grew up in the city.
Many roads inside Wilmington are still passable for residents who defied evacuation orders to ride the storm out.
But a city-wide curfew has been extended after five people were arrested on suspicion of looting from a store in the city on Saturday.
At least 17 people are now reported to have died in storm-related incidents in North and South Carolina since Florence made landfall as a category one hurricane on Thursday.
It has now weakened into a tropical depression with winds of 55km/h, according to the National Hurricane Centre.