In its 5 p.m. EDT update, the National Hurricane Center in Miami said Kirk was rapidly gaining strength about 1,065 miles northeast of the Northern Leeward Islands and about 1,505 miles west-southwest of the Azores. The storm had top sustained winds of 90 mph and was moving north-northwest at 13 mph.
No coastal watches or warnings were posted.
Forecasters said Kirk was expected to follow its current track Thursday night before turning toward the north Friday and then gaining forward speed as it turns toward the north-northeast by Friday night.
Hurricane force winds extended outward as far as 15 miles from Kirk's center, and tropical storm force winds extended as far as 70 miles.
Tropical Storm Leslie was about 1,060 miles east of the Windward Islands with top sustained winds of 45 mph and was moving west at 21 mph.
No coastal watches or warnings were in effect.
Leslie was expected to lose forward speed and move toward the west-northwest during the next couple of days, forecasters said.
The storm could become a hurricane in the next day or two.