Meanwhile, rescuers are scrambling to save 1,500 people stranded by flooding in the eastern North Carolina city of Lumberton.
"We have people on roofs (there) as we speak," McCrory said. The Federal Aviation Administration has ordered flight restrictions over the area so helicopters can rescue them.
But those aren't the only problems Matthew left behind.
Massive power outages
About 500,000 structures in North Carolina don't have power Monday.
"That's probably well over 1 million people without power," McCrory said. "That's 10% of our population in North Carolina -- all in a very small area. At least 10%."
Matthew's damage exceeded expectations, Duke Energy said. The power company said it now has to rebuild parts of the electrical system. It said some of the hardest-hit areas "might be without power all week."
20 deaths in the US
The 10 deaths in North Carolina included some victims who drowned after driving onto flooded roads.
"I cannot stress more: If you see a road that's flooded, do not take your car through that road," Gov. McCrory said. "If you see a barrier, do not go around that barrier."
Matthew also claimed the lives of four people in Florida, three in South Carolina and three in Georgia.
In South Carolina, 66-year-old David L. Outlaw drowned when his wheelchair got pinned down in standing water at a nursing facility's courtyard, Richland County Coroner Gary Watts said.
The US deaths came after Matthew devastated parts of the Caribbean, killing more than 300 people in Haiti, said Paul Altidor, Haitian ambassador to the United States.
Others report much higher death tolls in Haiti. Reuters said more than 800 people died in the impoverished country, citing local civil protection officials.
More 'catastrophic flooding' on the way
Forecasters warned of more "catastrophic flooding" as North Carolina residents braced for swollen rivers to top their banks in the next few days.
"River levels will rise above major flood stage this morning and remain elevated well into next week," the National Weather Service said.
What to do next
As more storm victims return to their homes from Florida to North Carolina, it's critical to know how to come back safely.
In addition to avoided all flooded roads, keep an eye out for downed power lines and weakened bridges and roads that look like they might collapse, the National Weather Service said.
Once back home, "walk carefully around the outside of your home to check for loose power lines, gas leaks and structural damage," the NWS said. "Stay out of any building if you smell gas."
The agency said carbon monoxide poisoning is one of the leading causes of death after storms involving power outages.
"Never use a portable generator inside your home or garage," the NWS said. "Use battery-powered flashlights. Do not use candles. Turn on your flashlight before entering a vacated building. The battery could produce a spark that could ignite leaking gas, if present."
North Carolina's Department of Public Safety offers additional tips on how to safely remove trees and limbs from homes.