The slow-moving, but punishing, Tropical Storm Melissa that has already killed four people is threatening catastrophic flooding across the northern Caribbean as it strengthens towards Jamaica.

Melissa is expected to become a major hurricane, possibly by later Saturday or Sunday, before making landfall across central Jamaica on Tuesday, with forecasters warning the system could dump up to 89 centimetres of rain (35 inches) across Haiti.

The storm's crawling pace - moving at just 5 kilometres (3.1 miles) per hour on Friday - means Jamaica could endure hurricane conditions for more than 72 hours, while southwestern Haiti faces what forecasters describe as life-threatening flash flooding.

Three people have died in Haiti, including two killed in a landslide in Port-au-Prince and another struck by a falling tree in Marigot, officials said. A fourth person was killed in the Dominican Republic, where another remains missing.

Jamaica's Meteorological Service principal director Evan Thompson told The Gleaner that residents should brace for a "double effect" as the hurricane's eye passes over the island, with the strongest winds hitting from opposite directions on either side of the centre.

The forecast marks a significant shift from earlier in the week, when landfall was considered only a "slim chance".

Authorities have readied more than 650 emergency shelters across Jamaica and said airports will close once a hurricane warning is declared. Prime Minister Andrew Holness warned the public to treat the approaching storm as a serious threat. "Take all measures to protect yourself," he said.

The storm has already wrought havoc in the Dominican Republic, where nearly 200 homes have been damaged and more than half a million people left without water.

In the Los Rios neighbourhood of the capital, Santo Domingo, families were forced to flee rising floodwaters on Thursday evening after surrounding streams burst their banks, according to the Listin Diario daily newspaper.

More than two dozen Dominican communities remain cut off by floodwaters, prompting mandatory evacuations and nationwide school closures.

The situation is particularly dire for thousands displaced by gang violence in Port-au-Prince, now living in makeshift shelters with scant protection. "I'm dealing with two storms: the gangs and the weather," Nephtali Johnson Pierre told The Associated Press news agency.