The service said county officials reported the dam's "imminent failure" at around 9:30 p.m. Thursday.
"The worst case scenario if that dam does breach, officials are anxious it might, is that water would go surging downhill into Lynchburg and it could drown that city in 17 feet of water in about 7 minutes".
The city's Department of Emergency Services urged people living on a number of roads near the dam to evacuate Thursday night.
The NWS issued a flash flood watch for the area that lasts until 11 a.m. Friday.
The deluge of rain that affected much of Virginia on Thursday, causing road closures and power outages in the Shenandoah Valley, has prompted evacuations in Lynchburg, just below an overflowing dam.
Authorities said concerns about the dam's failure will continue to be a threat until the water levels can safely be lowered.More news: Milestones: Apple's road to being a trillion-dollar enterprise
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Lynchburg has a population of about 80,000 and lies in the Blue Ridge Mountains.
In 2011, Virginia's Department of Conservation and Recreation identified the College Lake Dam as one of the state's "high-hazard" dams.
Turner Perrow, a member of the Lynchburg City Council who is also a civil engineer, tells NPR that the dam presents "a complicated problem".
Residents in the Virginia city of Lynchburg were ordered to evacuate their homes amid fears Friday morning that a dam could fail and flood the city.
City crews inspect the dam weekly because of its age. The lake behind it is filled with silt, which complicates potential solutions - if they removed the dam, for instance, they would need to ensure that the silt didn't cause other problems downstream.
Four to six inches of rain were said to have fallen overnight. The city owns the dam, but the university owns the lake.