Tropical Storm Lili heads for Cuba

This road in eastern Jamaica was a river of mud and flood water Sunday.

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RELATED Site: National Hurricane Center  CNN.com's Special report: Hurricanes  Tropical Storm Lili At 11 p.m. ET Sunday Latitude: 19.2 degrees north Longitude: 78.5 degrees west Position: 60 miles north-northeast of Montego Bay, Jamaica Next advisory:  5 a.m. ET

MIAMI, Florida (CNN) -- Tropical Storm Lili strengthened Sunday as it moved past Jamaica and aimed for Cuba, which is still reeling from Hurricane Isidore's damaging visit last week.

At 11 p.m. ET, Lili was 60 miles north-northeast of Montego Bay, Jamaica, and was moving to the west-northwest at 6 mph. Forecasters said its current track would bring it near the Cayman Islands and southern Cuba.

Lili's maximum sustained winds have increased to 65 mph, and National Hurricane Center forecasters said it could reach hurricane strength in the next 24 hours. A storm becomes a hurricane when its top winds hit 74 mph.

Within 72 hours, the storm should be over the Gulf of Mexico and heading toward the U.S. Gulf Coast with the potential to become a "significant hurricane," forecasters warned.

Lili could make landfall on the southern coast of western Cuba late Monday or early Tuesday. Forecasters said Lili's heavy rains could reach eastern Cuba late Sunday, bringing the potential for life-threatening flash floods and mudslides.

The government of Cuba issued a hurricane watch for the western provinces of Matanzas, Ciudad de la Habana, La Habana, Pinar del Rio and the Isle of Youth. The government of the Cayman Islands also issued a hurricane watch for all of the Cayman Islands.

The entire island of Jamaica was under a tropical storm warning, along with the Cuban provinces of Camaguey, Las Tunas, Granma, Santiago de Cuba, Guantanamo and Holguin.

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

Jamaica and the southwestern peninsula of Haiti were deluged Saturday with heavy rains, as they were just a week ago when Hurricane Isidore rammed through just south of Lili's current track. The rains are expected to gradually spread over the Cayman Islands and Cuba.

Meanwhile, far out to sea, Tropical Storm Kyle remained poorly organized Sunday, with maximum winds near 45 mph, according to the 11 p.m. ET update.

Kyle, the Atlantic season's third hurricane, became disorganized and dropped to tropical storm strength Saturday.

So far, the storm was not threatening to make landfall. At last report, it was stationary, about 240 miles south of Bermuda.

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