The storm could grow into a hurricane by Friday and a major one by the late weekend.

Tropical Storm Melissa is threatening the Caribbean Sea islands with dangerous landslides and life-threatening flooding, as officials urge residents of flood-prone areas to seek higher ground and shelter.

Jamaica’s eastern region could see up to 12 inches (300mm) of rain. “Now that is significant rainfall, and that is the main thing that we should be mindful of at this time,” Evan Thompson, director of Jamaica’s Meteorological Service, said.

Similar rainfall amounts were expected for southern Haiti and the southern Dominican Republic through Saturday, with even more rain possible locally, depending on Melissa’s path later in the week.

Heavy rain was also forecast for western Jamaica, southern Hispaniola, Aruba and Puerto Rico.

Melissa had maximum sustained winds of 50mph (85km/h) and was moving west at 2mph (4km/h) late on Wednesday night, according to the US National Hurricane Center in Miami.

The slow-moving storm was centred about 335 miles (535km) south-southwest of Port-au-Prince, Haiti, and some 295 miles (475km) south-southeast of Kingston, Jamaica.

The NHC said the storm could strengthen gradually in the coming days and grow into a hurricane by Friday and a major hurricane by the late weekend.

Heavy rains in the Dominican Republic have already disrupted traffic and led to the cancellation of sports events.

Melissa is the 13th named storm of the Atlantic hurricane season, and the first named storm to form in the Caribbean this year.

The National Oceanic and Atmospheric Administration predicted an above-normal Atlantic hurricane season – which runs from June 1 to November 30 – with 13 to 18 named storms.

Of those, five to nine were forecast to become hurricanes, including two to five major hurricanes, which pack winds of 111mph or greater.