(CNN) -- Tropical Storm Ernesto churned across the Caribbean Sea on Saturday, regaining some strength even as forecasters expect it to grow more powerful and emerge as a Category 1 hurricane in the next few days, the National Hurricane Center said.
That means that by the time it likely passes south of Jamaica on Sunday evening, Ernesto could pack sustained winds in excess of 74 mph. As is, the Miami-based weather center reported in its 8 p.m. advisory that the storm had regular winds of 60 mph and even more potent gusts.
Ernesto had weakened somewhat earlier Saturday, but leveled off through the middle of the day and then got even stronger.
By Saturday night, tropical-storm-force winds, at 39 mph or stronger, could be felt up to 140 miles for the storm's center about 260 miles south-southwest of Santo Domingo, Dominican Republic, and 435 miles east-southeast of Kingston, Jamaica.
The Jamaican government has issued a tropical storm warning for the Caribbean island, meaning such conditions are expected there some time over the next 36 hours.
The storm could bring three to six inches of rain, if not more, to Jamaica by the time it's gone, the hurricane center said. Residents and visitors on other Caribbean islands such as Aruba, Curacao and Bonaire could also find themselves getting drenched.
"Some strengthening is possible during the next 48 hours and Ernesto could become a hurricane during the next day or so," the hurricane center said of Ernesto at 8 p.m., when it was spinning west at an 18 mph clip.
The storm is forecast to enter the Gulf of Mexico on Thursday morning, by which time it is expected to be back to tropical storm status, according to forecasters.
"Past Thursday, we will be monitoring this storm very closely for further development in the Gulf," CNN meteorologist Sarah Dillingham said.
Ernesto is not the only tropical threat forecasters are monitoring.
Tropical Storm Florence strengthened a bit Saturday over the open Atlantic Ocean, its center about 515 miles west of the Cape Verde Islands as it headed toward the Leeward Islands.
At 5 p.m. Saturday, the storm was heading west-northwest at a 15 mph rate and had sustained winds of 50 mph, a shade weaker than Ernesto. It could gain more strength over the next few days, the hurricane center said.