GRIFTON - Catastrophic floods raised the threat of dam breaks and landslides across the southeastern United States on Sunday, prolonging the agony caused by a killer hurricane that has left more than a dozen people dead and billions of dollars in damage.

Downgraded to a tropical depression, 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.

"A lot of people have evacuated already," said Denise Harper, a resident of Grifton, a small North Carolina town threatened by rising water levels in a nearby creek and the River Neuse. "It's worrying to watch the water slowly rising."

Local media have tallied 13 deaths since Florence made landfall Friday as a Category 1 hurricane near Wrightsville Beach, North Carolina -- with ten deaths confirmed by officials in that state alone. "Unfortunately we've still got several days to go," Brock Long, administrator of the Federal Emergency Management Agency, told Fox News.

Long said more havoc lays ahead as the storm broadens its geographic scope over regions deeply saturated with water. Of particular concern were the risks to dams, already stressed by heavy rainfall from a tropical storm earlier in the month, he said, urging citizens to heed official warnings about what was now a "flood event."

"What we have to focus on are there any dams that are going potentially going to break. People fail to heed warnings and get out or they get into the flood waters trying to escape their home. And that's where you start to see deaths escalate," he told CBS News. "Even though hurricanes are categorized by wind, it's the water that really causes the most loss of life."

A dull, leaden sky hung over Grifton on Sunday. Days of heavy rainfall have turned the surrounding farmland into soggy marshland. Grifton fire chief Justin Johnson warned of more deluges in the days ahead. "People who need to be evacuated have been evacuated. We continue to patrol the area, but people have already been through Matthew hurricane and know what to expect," he told AFP.

Harper recalls Hurricane Floyd in 1999. "We got cut off, there was nowhere to go, water everywhere, the military had to come to bring us some food," she said.

ELECTROCUTION RISK

North Carolina Governor Roy Cooper told reporters "the strongest storm bands are dumping two to three inches of rain (5 - 7.5 centimeters) per hour" over regions that had already received up to two feet of rain. "That's enough to cause flooding in areas that have never flooded before until now. The risk is growing as well in the mountains, where rains could lead to dangerous landslides," he said.

A woman and her baby were among the storm's first casualties when a tree fell on their house. Others killed included three who perished "due to flash flooding and swift water on roadways," according to the Duplin County Sheriff's Office, and a 61-year-old woman who died when her car hit a downed tree.

At least two people died from electrocution while attempting to connect their generators while one couple died of monoxide poisoning from running their generator indoors, according to reports.

'BILLIONS' IN DAMAGE

Even as some residents began returning to their homes, officials warned of a long road to recovery ahead. "I think that the storm is likely going to produce impacts greater than Hurricane Matthew," Senator Thom Tillis of North Carolina said on Fox News, referring to a Category 5 storm that struck in 2016, killing 26 in the state.

"The agriculture industry, the largest industry in our state is hard-hit. We will have to sort out the crop damage," he continued, adding: "I think that it's fair to say in terms of economic impact rebuilding that we are talking in the billions of dollars."

The number of customers without power across North Carolina fell slightly to 700,000. Fifteen thousand meanwhile were being housed in 158 shelters across the state. US Coast Guard Commandant Admiral Karl Schultz meanwhile told ABC 28 aircraft had been deployed as well as 35 "shallow water rescue teams."

Some 2,800 North Carolina National Guardsmen were actively aiding rescue and relief efforts Sunday with another 1,000 on standby. 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.