This satellite image shows weather systems Sunday, Nov. 3, 2024. NOAA via AP

SAN JUAN, Puerto Rico — Tropical Storm Rafael chugged past western Jamaica on Tuesday and was expected to strengthen into a hurricane as it headed toward Cuba.

The storm was located 105 miles east of Grand Cayman in the Cayman Islands on Tuesday after passing by Jamaica, where little damage was reported. It was picking up speed with maximum sustained winds of 70 mph and was moving northwest at 15 mph, according to the National Hurricane Center in Miami.

The center said it expected “steady to rapid intensification” over the next 24 hours. It was expected to pass over or by the Cayman Islands on Tuesday night and make landfall in western Cuba on Wednesday.

“Rafael is expected to become a hurricane as it passes near the Cayman Islands with further strengthening before it makes landfall in Cuba,” the center said.

The U.S. State Department issued an advisory for Cuba on Tuesday afternoon, offering departure flights to non-essential staff and American citizens, and advising others to “reconsider travel to Cuba due to the potential impact of Tropical Storm Rafael.”

Meanwhile, on Tuesday morning, the Cuban Civil Defense called on Cubans on social media to prepare as soon as possible, because when the storm makes landfall “it’s important to stay where you are.” The day before, authorities said they had issued an evacuation order for 37,000 people in far eastern Cuba, in the province of Guantanamo, due to bad weather.

A hurricane warning was 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 was in effect for the Cuban provinces of Villa Clara, Cienfuegos, Sancti Spiritus and Ciego de Avila, as well as the lower and middle Florida Keys from Key West to west of the Channel 5 Bridge, and Dry Tortugas. The warning was lifted in Jamaica after the storm passed by the western coast. A tropical storm watch was in effect for the Cuban provinces of Camaguey and Las Tunas.

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

In the Cayman Islands, officials closed schools and government offices as they urged residents to prepare. Long lines were reported at grocery stores as the storm approached.

The storm is bad news for Cuba, which 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 in parts of Cuba and the Cayman Islands.

Heavy rainfall also was expected to spread north into Florida and nearby areas of the southeast U.S. during the middle to late part of the week. The Hurricane Center predicted storm surges in Florida could reach 1 to 3 feet in Dry Tortugas and 1 to 2 feet in the Lower Florida Keys. A few tornadoes also were expected Wednesday over the Keys and southwesternmost Florida mainland.

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.