The new tragedy comes just days after Typhoon Mangkhut pounded the nation's north with heavy winds and rain, sparking a separate landslide that left dozens dead.
Florence slowly crawled over South and North Carolina, dumping heavy rains on already flood-swollen river basins that authorities warned could bring more death and destruction.
The centre of Florence is expected to hit North Carolina's southern coast on Friday, then drift southwest before moving inland on Saturday.
The wet weather was the first farmers in some areas had seen for more than a year, and even included hail.
Dozens of people are missing and 1.2 million are sheltering in the camps, state officials said, as water receded and a huge clean-up gathered pace.
At least 22 people were killed and five critically injured in Tuesday's collapse of a motorway bridge running over the north-western Italian port city of Genoa.
Oman News Agency reported that the cyclone will intensify within 12 hours.
Heavy rain over the last 24 hours has blocked roads and disrupted traffic in South Africa's drought-hit Cape Town, city officials said on Thursday.