A Navy statement says the decision comes after inspections of the region's port and airfield.
Evacuation orders have been lifted in several coastal SC counties as Florence continues to dump rain on the state.
Although Brunswick County is under mandatory evacuation, Ingram said some people made a decision to stay in their homes.
Floyd County officials asked residents in flood prone areas to voluntarily evacuate Saturday. Radar showed parts of the sprawling storm over six states, with North and SC in the bull's-eye.
The total extent of devastation from Florence, which has turned from a hurricane into a tropical storm, remains unknown as rain and flooding continue to wreak havoc in the Carolinas.
The National Hurricane Center's forecast for Florence as of 11am Saturday.
The storm's extremely slow speed means the risk of catastrophic flooding remains high across both states.
Atlantic Beach on North Carolina's Outer Banks islands had already received 30 inches of rain, the U.S. Geological Survey said.
In a separate briefing, Steve Goldstein of the National Oceanic and Atmospheric Administration (NOAA) said some areas have already received two feet of rain and could expect up to 20 inches more as the system moved "slowly, almost stationary" over eastern North Carolina.
About 809,000 of those customers are North Carolina, and about 155,000 are in SC.
Photos and videos from around the region, and particularly North Carolina, showed the power that Florence contained as it came ashore, leading to rescues across the area.
Serious flooding is expected in inland areas of the two states, with waters already rising in communities such as Conway, South Carolina, near Myrtle Beach - and some rivers may not crest for another three to five days. Maximum sustained winds remained at 50 miles per hour (80 kph).
But just how slow is the storm moving?
Members of Onslow County emergency look to see if a passenger was still in a auto that was overtaken by flooding on US Route 17 outside of Jacksonville, North Carolina. Hikers have been told to seek shelter off the Appalachian Trail to avoid falling trees, flash floods and mudslides.
A 78-year-old man in Kinston, North Carolina, was electrocuted when he tried to connect two extension cords outside in the rain, according to Lenoir County Emergency Services Director Roger Dail.
The National Weather Service says the worst flooding will likely start Saturday night or Sunday morning and will continue for several days.
Florence was packing 120mph winds (193km/h) on Thursday but weakened from a Category 3 hurricane to Category 1 before it hit the coastline on Friday.
He said "24 to 36 hours remain for significant threats" from heavy rain, storm surges and flooding.
North Carolina Gov. Roy Cooper called Florence an "uninvited brute" that could wipe out entire communities as it grinds its way across land. The storm is some 645 kilometres wide. Power outages are widespread including over 740,000 in North Carolina and 163,000 in SC.
That's on top of the hundreds of rescues made by volunteer groups or individuals helping each other. In South Carolina, a 61-year-old woman was killed when her vehicle hit a tree that had fallen across a highway.
At least seven people, including a mother and her baby, have been killed by Florence, which was initially categorised as a hurricane with 120mph winds.
Five of the six deaths officials have thus far linked to the storm all occurred in North Carolina on Friday.