The storm was sporting winds of up to 50 mph about 235 miles east of Cabo Gracias a Dios on the Nicaragua/Honduras border, the National Hurricane Center in Miami said in its 11 p.m. EDT advisory. It was heading westward at 15 mph.
A tropical storm warning was in effect for Jamaica and a watch was in place for Grand Cayman and the coast of Honduras from its border with Nicaragua westward to Punta Castilla, the hurricane center said.
People in Belize and the Yucatan Peninsula of Mexico should monitor Ernesto's progress, the center said.
A decrease in the storm's forward speed was expected in the next two days, the center said, and the center of the storm was expected to pass to the south of the Cayman Islands Sunday night.
Monday it was expected to move north of Honduras.
Tropical storm winds extended outward up to 125 miles from the storm center. Some strengthening is possible in the coming days, the center said.
Meanwhile, the winds produced by Tropical Storm Florence, which was about 925 miles west of the Cape Verde Islands at 11 p.m. EDT Sunday, had weakened from 60 mph winds earlier in the day to 40 mph as it moved west-northwest across the Atlantic Ocean at 13 mph, forecasters said.
Florence, which is expected to deteriorate into a tropical depression Monday and pick up forward speed during the next two days, presented no danger to any land masses, the center said. Florence was producing tropical storm-force winds up to 60 miles from its center.