The storm was moving west-northwest at 14 miles per hour and had maximum sustained winds of 50 miles per hour.
NHC said that little change in strengthening is forecast until Kirk crosses the Lesser Antilles, followed by weakening over the eastern Caribbean Sea. Rosa has maximum sustained winds of 125 mph and was located about 570 miles southwest of the southern tip of the Baja California Peninsula.
From late Friday and into this weekend, clusters of showers and thunderstorms have the potential to bring localised flash flooding to the United States and the British Virgin Islands, Puerto Rico, the Dominican Republic and Haiti.
A tropical storm warning is in effect for: Barbados, St. Lucia, Dominica, Martinique and Guadeloupe.
NOTE: A Hurricane Warning can remain in effect when dangerously high water or a combination of dangerously high water and exceptionally high waves continue, even if the winds have subsided below hurricane intensity.
The number of Tropical Storms and Hurricanes increases substantially in August, peaks in mid-September and decreases towards a minimum by early November.
"We don't believe Cayman will be impacted with the winds associated with Tropical Storm Kirk, but we do expect moisture", Mr. Miller said.
NHC predicts Kirk will approach Barbados and the northern Windward Islands Thursday afternoon and move into the eastern Caribbean Sea by Friday morning. It has a 90 percent chance of development in the next five days.
These islands, as well as St. Lucia, Martinique and Dominica, can expect tropical storm conditions.
A Tropical Storm Warning means that tropical storm conditions are expected somewhere within the warning area within 36 hours.
The complex area of low pressure that includes what's left of Subtropical Storm Leslie is organizing in the middle of the Atlantic Ocean. The NHC said these rains may produce life-threatening flash floods and mudslides.