Florence is no longer a tropical storm. It has weakened into a depression, according to the National Hurricane Center.
The center says, however, that "flash flooding and major river flooding will continue over a significant portion of the Carolinas."
"This is still a catastrophic, life-threatening storm," said hurricane center meteorologist Zack Taylor about Florence, which has claimed at least 12 lives.
After the heaviest rain leaves the area, the flood disaster will likely persist for days, if not weeks longer, as rivers will remain severely out of their banks.
As Florence continues its slow crawl, it will produce "heavy and excessive rainfall" in central and western North Carolina into far southwest Virginia; southern North Carolina into northern South Carolina; and west-central Virginia, north of Roanoke and west of Charlottesville.
The hurricane center also says a few tornadoes are possible Sunday across North Carolina and eastern South Carolina.
The remains of Florence are expected to pick up speed as they head northward later Sunday and Monday, eventually reaching the northeast U.S. before heading out to sea.
The large storm came ashore earlier in the week as a hurricane, flooding rivers, forcing high-water rescues and leaving a trail of destruction.
North Carolina Gov. Roy Cooper said Saturday that despite the downgrade, Florence was still "unloading epic amounts of rainfall" and still very capable of wiping out entire communities.
"The flood danger from this storm is more immediate today than when it made landfall," he said. "We face walls of water at our coast, along our rivers, across farmland, in our cities and in our towns."
Cooper said floodwaters were continuing to rise, and he urged evacuees to "stay put" until they received "the official all-clear."
Gov. Henry McMaster of South Carolina said Saturday that President Donald Trump had assured him "he would do whatever it takes to see that everything is available" in terms of federal resources for South Carolina as it coped with the onslaught and aftermath of Florence.
McMaster said record amounts of rainfall in the Carolinas had been measured — "in feet, in some places, and not inches" — and warned that in addition to the extra rainfall, South Carolina would have to handle flooding from North Carolina that was moving downriver.
Hundreds of people in North Carolina have been rescued from rising water. Authorities said they had received more than 150 telephone calls to rescue people in the historic town of New Bern alone because water had entered their homes.
Shaken after seeing waves crashing on the Neuse River just outside his house in New Bern, restaurant owner and hurricane veteran Tom Ballance wished he had evacuated.
“I feel like the dumbest human being who ever walked the face of the Earth,” he said.
New Bern resident Latasha Jones was one of the more fortunate ones.
“The evacuation was countywide, but since we’re not in a flood zone, we weren’t really worried about that,” she told VOA.
“The way our house sits, it’s elevated. We have steps on the sides of the house, so it’s a few feet off the ground anyway. And since we’re already on high ground, those two things together kind of help insulate us a little more than, I would say, others,” she said.
Some information for this report came from The Associated Press.
WATCH: Hurricane Florence Comes Ashore