After submerging North Carolina with almost 3 feet (1 metre) of rain, the storm dumped more than 6.5 inches (16.5 centimetres) of rain in the Northeast, where it caused flash flooding, wind damage and prompted at least one tornado warning, the weather service said.
Trump's visit will also include stops in both North and SC, where White House Press Secretary Sarah Sanders said that the president will hear from a "pretty large delegation". "There will be nothing left undone", he said. "You'll have everything you need".
Florence also left mass flooding throughout the state and hundreds of thousands without power.
He was accompanied by Homeland Security Secretary Kirstjen Nielsen, Federal Emergency Management Agency chief Brock Long, Senators Richard Burr and Thom Tillis of North Carolina and Senators Lindsey Graham and Tim Scott of SC.
The water level of the Cape Fear River was expected to crest at 61.8 feet by Tuesday. That has disrupted efforts to restore power, clear roads and allow evacuated residents to go home.
All areas around the river, within one mile, are under a mandatory evacuation.
It's too early to tell how many people will end up homeless because of Florence.
In North Carolina, transportation officials Tuesday continued advising motorists who ordinarily might take southbound I-95 from Virginia to SC that flooding has made long sections of I-95 in North Carolina impassable.
Authorities say two female inmates being transported to a mental health facility in SC drowned in rising flood waters after the van they were in was swept away.
The Transportation Department advised northbound motorists to take a wide detour around the area by using I-85 from Georgia through South Carolina's Upstate and on to Charlotte.
The National Weather Service said in a tweet Tuesday that many rivers in the Carolinas are in flood stage and still rising, and the "flooding could last weeks". Residents in the nearby town of Conway worry that's going to send water from the rising Waccamaw River to flood their homes instead.
As of Tuesday evening, the storm had been blamed for at least 35 deaths. Trump said, without offering evidence, that Democrats had inflated the figure to make him look bad. Critics said the Trump administration was slow to recognise the extent of the damage and slow to help. He contributed $1 million each to the American Red Cross and Foundation For The Carolinas' Hurricane Florence Response Fund.