It left people trapped in flooded homes as it caused carnage in North and SC and Virginia.
State officials are asking interstate travelers not to drive through North Carolina.
Three died in one inland county, Duplin, because of water on roads and flash floods, the sheriff's office said.
Tropical Storm Florence weakened to a tropical depression early Sunday, but significant portions of North and SC were expected to remain vulnerable to flash flooding and major river flooding, forecasters said.
Governor Cooper advised North Carolina residents inland that rivers will rise days after the rain has stopped.
As rivers swelled toward record levels, state regulators and environmental groups were monitoring the threat from big hog and poultry farms located in low-lying, flood-prone areas.
The national meteorological center says southern China "will face a severe test caused by wind and rain" and urged officials to prepare for possible disasters. In the Philippines, dozens of people, mostly miners and their families, are feared trapped by a landslide triggered by the typhoon in a mountain province.
North Carolina Governor Roy Cooper said the storm was posing an even greater risk of flooding than when it first made landfall.
While local residents may have felt some minor relief that a more severe storm would not hit the coastline, Florence was still projected to carry well into southeast North Carolina and into the heart of northeast SC.
- New images are pouring in as Tropical Strom Florence unleashes risky flooding Across North Carolina.
Charles Rucker, a retired teacher, had only spent five nights in his newly-purchased house, built in 1830, when Florence struck.
Colleen Roberts, city public information officer for the area, told BBC World News more than 4,000 homes had been "destroyed or completely damaged" there, based on calls they had received for emergency services.
Almost 800,000 people are without power, majority in North Carolina, according to the Associated Press. SC recorded its first death from the storm, with officials saying a 61-year-old woman was killed when her vehicle hit a tree that had fallen across a highway.
Two other men were killed in Lenoir County, North Carolina - electrocuted in separate incidents, according to CNN.
Of the 13 victims, nine died on Friday night, while the rest were killed on Saturday, according to the officials.
The White House said President Donald Trump approved making federal funding available in some affected counties.
About 760,000 customers are without power in North Carolina on Saturday.
But it continued to warn of "catastrophic" flooding from excessive rainfall.
The military announced Saturday it was deploying almost 200 soldiers to assist in storm-related response and recovery efforts, along with 100 trucks and equipment.
"We have completed all of our water rescues & want to sincerely thank all of the volunteers who helped us save lives".
As Florence lingers over east SC, officials are keeping an eye on areas prone to flooding.
A spokesman for the South Carolina Highway Patrol warned on Saturday that conditions remained treacherous on roads.
Mayor Mitch Colvin told people living within a mile of the region's main river, the Cape Fear, or the nearby Little River, that they had until 3 p.m. Sunday to get out. It said it was located about 50 miles (65 km) west of Myrtle Beach, South Carolina, and forecasters predicted a slow westward march. They wanted a drink'.
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