The center was located approximately 20 miles southwest of Columbia, South Carolina, as of 5 a.m.
Downgraded to a tropical depression, Florence was still massive.
Besides federal and state emergency crews, rescuers were being helped by volunteers from the "Cajun Navy" - civilians equipped with light boats, canoes and air mattresses - who also turned up in Houston during Hurricane Harvey to carry out water rescues.
That's just the number of customers without power in the Carolinas.
Authorities have warned that flash flooding and major river flooding are expected to continue over large parts of the Carolinas.
The heaviest rains should shift to between northern SC and west-central North Carolina during the day.
It has dumped up to 40 inches (100 cm) of rain on North Carolina since Thursday and continued to produce heavy rain over much of North Carolina and eastern SC, the NWS said.
SC also has a new record for rainfall in a single tropical system. Harvey dropped 60.58 inches of rain previous year in Texas, setting the state's new record. The 30.59 inches that have fallen in Swansboro sets a new record for North Carolina.
Members of a combined New Bern/Greenville swift water rescue team Brad Johnson, left, and Steve Williams rest after searching for people stranded by floodwaters caused by the tropical storm Florence in New Bern, N.C., September 15, 2018. Some of the heavier bands have shifted toward Fayetteville, Charlotte and Raleigh.
The rain may be particularly heavy in the mountains, where there is an elevated risk of flash flooding.
More than 15,000 people were staying in 150 emergency shelters in North Carolina on Sunday.
More catastrophic flooding is predicted there as well.
Images captured by Associated Press journalists show flooding caused by Florence in the Carolinas and Typhoon Mangkhut in the Philippines.
Torrential rain from Florence is now causing rapid rises in area rivers.
And in Lumberton, North Carolina - a city submerged by Hurricane Matthew in 2016 - residents are bracing for potential disaster as the Lumber River threatens to burst through a recently patched-up gap in the levee system.
Weakened to a tropical depression early Sunday after blowing ashore as a hurricane with 90 miles per hour (145 kph) winds on Friday, Florence was still spinning slowly atop the Carolinas as it pulled warm water from the ocean and hurled it onshore. That would top the record-setting level of 23.51 feet reached during Floyd. "More and more inland counties are issuing mandatory evacuations to get people to safety quickly". The town had 4 1/2 feet of storm surge.
"If the river rises to the level they say it's going to, then this warehouse is going to be under water", he said. This will cause devastating flooding across much of Onslow County with travel made impossible and many homes completely flooded. As the river kept rising Sunday, he knew it was time to flee.
In New Bern, a riverfront city near North Carolina's coast, the storm tore away porch steps, splintered balconies and sent a yacht plowing into a garage that shattered like kindling.
Florence is still moving very slowly inland. Florence will likely become a remnant low within 36 hours.