The Miami-based National Hurricane Center (NHC) said the storm was about 80 kilometres north of Havana at 0001 GMT today, moving north at 28 miles per hour with maximum sustained winds of 40 miles per hour.
On the forecast track, Philippe's centre will swiftly cross the Straits of Florida, "and move across the Florida Keys or the southern tip of the Florida peninsula overnight, and across the northwestern Bahamas Sunday morning," the NHC said.
The Hurricane Center also warned that brief tornadoes were possible across portions of South Florida.
Cuban Civil Defense earlier warned citizens of a storm -- at the time a tropical depression -- bringing strong wind and heavy rain, and causing large ocean swells.
"Since it is a weak system its center is not important," the Institute of Meteorology (Insmet) said, but warned of heavy rain from the western state of Matanzas to central Cuba.
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