Joaquin was packing maximum sustained winds of 130 miles (215 kilometers) per hour and could grow even stronger over the next 24 hours, the National Hurricane Center said.
"On the forecast track, the core of strongest winds of Joaquin will move near or over portions of the central Bahamas and pass near or over portions of the northwestern Bahamas on today," the NHC said in its 0100 GMT bulletin.
The NHC described Joaquin as a large storm moving at only five miles (seven kilometers) per hour.
The storm has potential for life-threatening damage, and on its current path was likely to cause coastal flooding in the mid-Atlantic US region, forecasters said.
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Cuban officials issued a tropical storm warning for much of the south-eastern part of the island, meaning that hurricane conditions are expected somewhere within the warning area.
Emergency preparations began as far north as New York, and officials in the Bahamas urged people to brace for up to 15 inches (37 centimeters) of rain.
Classes were called off in the Bahamas, some flights were cancelled and cruise ships headed for the popular vacation destination were diverted elsewhere.
Residents of the eastern US cleared grocery shelve of water, milk and other essentials before the storm's arrival.
Since Joaquin is moving slowly "a catastrophic situation may unfold" in the Bahamas "with a prolonged period of intense hurricane conditions," according to www.Weather.Com.
Torrential rains are likely in the Carolinas and Virginia, US media reported.
A dangerous and life-threatening storm surge will raise water levels by as much as 10 feet above normal tide levels in parts of the central Bahamas, it said.