At least four people have died since Hurricane Florence crashed into the coast Friday and almost stalled.
Five of the six deaths officials have thus far linked to the storm all occurred in North Carolina on Friday. "We hope there are not more", Cooper said.
Florence flattened trees, buckled buildings and crumpled roads.
In North Carolina alone, there were 777,937 power outages as of 1:20 p.m. ET, according to North Carolina's Department of Public Safety.
Mother Lesha Murphy-Johnson and her baby, Zac, were killed after being trapped inside their home in Wilmington when a tree fell onto the roof at around 9.30am on Friday.
Two men in their 70s were killed in Lenoir County.
Cooper said others should not follow suit.
Florence's flooding claims a couple of cars and the first story of a house in New Bern, NC.
Hurricane Florence made landfall as a Category 1 storm in Wrightsville Beach, North Carolina, after stalking the Carolina coast for days.
But it was clear that this was really about the water, not the wind.
As of Saturday morning, at least six deaths have been blamed on the storm, nearly a million people were without power across North and SC, and some areas have already faced extreme flooding. The storm is some 645 kilometres wide. Forecasters predicted severe flooding for parts of southeastern North Carolina and northeastern SC starting Sunday.
One of the towns worst affected is New Bern, which sits between the Neuse and Trent rivers in North Carolina.
Authorities warned, too, of risks of mudslides and environmental disasters from floodwaters washing over industrial waste sites and hog farms.
Some parts of North Carolina have already seen surges as high as 10ft in places.
On Saturday morning, the 563-km-wide storm was strolling along at 3.2kmh, unleashing drenching downpours in eastern SC.
It came ashore Friday morning as a Category 1 hurricane.
Numerous roads across eastern North Carolina were blocked by fallen trees and flooding including parts of I-95, a major north-south artery. Another 30 sites in North and Carolina had at least 10 inches.
More than 360 people had been rescued by midafternoon Friday, hours after then-Hurricane Florence swept through, but another 140 were still waiting for help, city spokeswoman Colleen Roberts told The Associated Press.
Stream gauges across the region showed water levels rising steadily, with forecasts calling for rivers to crest Sunday and Monday at or near record levels. As we get closer toward the middle of next week, Florence's remnants should be near or spreading across our area.
United States correspondent Cordelia Lynch, who is in New Bern, said: "This community in the weeks and months to come is up against a great deal of flooding".
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.
"The wind was so hard, the waters were so hard ..."
Senate Minority Leader Chuck Schumer, D-N.Y., called Trump's tweets "shameful" and said the president owes "3,000 families in Puerto Rico an apology". Eventually, a volunteer rescue team from IN arrived with a boat and rescued them.
"Honestly, I grew up in Wilmington".