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The storm was packing sustained winds of 240 kilometers per hour as it moved west-northwest at 30 kilometers per hour, the NHC said at 1500 GMT.
"On the forecast track, the center of Jose will pass near or east of the northeastern Leeward Islands on Saturday," the NHC said.
Ocean swells "likely to cause life-threatening surf and rip current conditions" are expected to affect portions of the Leeward Islands later today, the NHC said.
Hurricane conditions are also possible on Caribbean islands including Antigua, Barbuda, and Anguilla today.
Jose follows Irma, a powerful Category Five hurricane tearing across the Caribbean towards to Florida.
Further west, Hurricane Katia was also upgraded today to a Category Two storm as it churned towards the eastern coast of Mexico.
Mexico's National Water Commission meteorological authority said Katia picked up strength as it swirled in the Gulf of Mexico 205 kilometers from the major port city of Veracruz.