Although the storm is passing north of Myrtle Beach, the concern now is that river water from North Carolina will flow into the area and combine with all the water that is already there.
Rescue crews in Onslow County helped evacuate 70 people from a Jacksonville hotel early Friday after the roof collapsed and rain rushed in.
Travel is extremely hazardous because of storm surge, Trogdon said, and will only get worse.
More than 20,000 people are staying in 157 emergency shelters in North Carolina, Cooper said.
The number of service members deployed include 7,500 from the US Coast Guard and 6,500 from the National Guard, the Federal Emergency Management Agency said.
The storm's centre was about 180km east of Wilmington, North Carolina, at 2pm local time (18:00 GMT) but tropical storm-strength winds and heavy rains already were hitting North Carolina's Outer Banks barrier islands.
Five deaths - a woman in Pender County, a mother and child in Wilmington and two people in Lenoir County - have been blamed on the storm.
In Wilmington, near where the eye of the storm touched down, trees and power lines were felled and many windows broken.
With rain pounding relentlessly, the streets were deserted.
Florence made landfall on the East Coast Friday morning with wind speeds of 195 miles per hour. "The longer you have this hurricane wind flow, the longer you push that water well inland", he said.
North Carolina's governor Roy Cooper said: "Know that water is rising fast everywhere, even in places that don't typically flood".
At 8 a.m. EDT, the Miami-based hurricane center said rainfall will continue to produce catastrophic flash flooding and prolonged significant river flooding.
Tropical storm-force winds extend outward up to 175 miles (280 kilometers) from its center.
A tornado watch was also in effect for parts of North Carolina. Wilmington Deputy Fire Chief Steve Mason said the victims died at the scene.
Florence was packing 120mph winds (193km/h) on Thursday but weakened from a Category 3 hurricane to Category 1 before it hit the coastline on Friday. "I wonder how it would have been with a Category 4 or 5".
"With having five kids and my husband's stuck at work on standby for his job at the hospital it was just easier for us to stay at our home where we have all of our things", she said. "But there are a lot of big trees around so we preferred to spend the night at a friend's to be sure".
"We're looking at the same amount of rainfall in three days".
A slowing tropical storm Florence continues to creep along the Carolinas today. As of Friday morning, more than a half a million people had lost power in North and SC.