Tropical Storm Rafael moved towards the Cayman Islands on Tuesday and was forecast to strengthen into a hurricane en route to Cuba.

The storm was located 105 miles (170km) southwest of Kingston, Jamaica, early on Tuesday. It had maximum sustained winds of 60mph (95kph) and was moving northwest at 13mph (20kph), according to the National Hurricane Centre in Miami.

“Rafael is forecast to become a hurricane in the northwestern Caribbean near the Cayman Islands with further strengthening before it makes landfall in Cuba,” the centre said.

The storm is expected to move near Jamaica on Tuesday morning, be near or over the Cayman Islands on Tuesday night and be near or over western Cuba on Wednesday.

A hurricane warning is in effect for the Cayman Islands and the Cuban provinces of Pinar del Rio, Artemisa, La Habana, Mayabeque, Matanzas and the Isle of Youth.

A tropical storm warning is in effect for Jamaica and the Cuban provinces of Villa Clara, Cienfuegos, Sancti Spiritus and Ciego de Avila.

A tropical storm watch is in effect for the Cuban provinces of Camaguey and Las Tunas and the Lower and Middle Florida Keys from Key West to west of the Channel 5 Bridge, as well as Dry Tortugas.

“The storm is currently situated in an atmospheric and oceanic environment that is quite conducive for strengthening,” the hurricane centre said.

Rafael is expected to pass near or over the Cayman Islands late on Tuesday, with officials closing schools and government offices as they urged residents to prepare.

Jamaica also closed down as a precaution, with the storm’s outer winds battering the island late on Monday.

Rafael was forecast to approach Cuba on Wednesday. Cuban authorities said on Monday night that some 37,000 people are under evacuation orders in far eastern Cuba, in the province of Guantanamo, because of bad weather.

The island is still struggling to recover from Hurricane Oscar, which battered the island about two weeks ago after making landfall in the eastern part of Cuba, killing at least six people. The storm also coincided with a large-scale blackout on the island.

Forecasters warned Rafael would unleash heavy rains across the western Caribbean that could lead to flooding and mudslides, with up to 10 inches (25cm) expected locally in Jamaica and parts of Cuba.

Heavy rainfall also was expected to spread north into Florida and nearby areas of the southeast US during the middle to late part of the week. A few tornadoes also were expected on Wednesday over the Keys and southwestern Florida.

Rafael is the 17th named storm of the season.

The National Oceanic and Atmospheric Administration predicted the 2024 hurricane season was likely to be well above average, with between 17 and 25 named storms. The forecast called for as many as 13 hurricanes and four major hurricanes.

An average Atlantic hurricane season produces 14 named storms, seven of them hurricanes and three major hurricanes.