PORT ROYAL, Jamaica — Fishermen near Jamaica’s capital tied their wooden skiffs down along a rocky shore Sunday as Tropical Storm Ernesto spun off the Caribbean country’s southern coast on a path that may carry it across the Yucatan Peninsula and into the Gulf of Mexico.

The rapidly moving storm brought heavy rainfall and gusty winds to the island Sunday, though US forecasters said it was becoming less organized.

Jamaica’s emergency management agency urged people in flood-prone areas to be on alert and to avoid flooded waterways and submerged roads. The government had earlier ordered fishermen on outlying cays to evacuate and move to the main island.

Ernesto was expected to dump 3 to 6 inches of rain on the Caribbean island of less than 3 million people before drenching the coasts of Honduras, Belize, and Mexico, possibly as a hurricane. Forecasters said it might weaken over land and then reemerge as a hurricane in the Gulf of Mexico late in the week.

A tropical storm watch was in effect for the coast of Honduras, from the border with Nicaragua westward to Punta Castilla, and the island of Grand Cayman in the Cayman Islands.

Showers and thunderstorms were also still possible over the Dominican Republic and Haiti, which share the Caribbean island of Hispaniola.