Images of the Category 4 storm's predicted path posted by the storm tracker show the states' coasts directly in the hurricane's path.
The storm is also poised to hit the Bahamas and has already hit the U.S. Virgin Islands.
NHC Director Ken Graham said in a Facebook Live briefing that Dorian's winds had reached speeds of up to 150 miles per hour.
President Trump cautioned those in the storm's path to "be safe" as the hurricane approaches the U.S. coastline.
"Looking like our great South Carolina could get hit MUCH harder than first thought. Georgia and North Carolina also," he tweeted Saturday morning. "It’s moving around and very hard to predict, except that it is one of the biggest and strongest (and really wide) that we have seen in decades. Be safe!"
Both Gov. Ron DeSantis (R) and Trump have declared a state of emergency in Florida.
The president's Friday declaration authorized the Federal Emergency Management Agency (FEMA) to coordinate disaster relief efforts.
Trump has insisted that his administration would be prepared to respond to the storm. He has faced criticism for his response to Hurricane Maria, which devastated Puerto Rico in 2017.
Trump this week rekindled a spat with Puerto Rican leaders over the response to Hurricane Maria in 2017.
The president blasted San Juan Mayor Carmen Yulín Cruz as “incompetent,” demeaned the island as “one of the most corrupt places on earth” and diverted FEMA funds toward the southern border even as his administration is expected to provide assistance to the U.S. territory in the wake of yet another large-scale storm.
Trump visited the Carolinas in 2018 after Hurricane Florence devastated parts of the southern states.
The storm caused lengthy power outages and severe flooding in parts of North Carolina and South Carolina after dumping significant rain on the two states.