A rapidly growing weather system brewing in the Gulf of Mexico was expected to bring heavy rain and flooding to South Florida and parts of Cuba on Friday and into the weekend, meteorologists said.

A tropical storm warning, bringing with it an elevated risk of extremely strong winds and heavy rain, was in effect across South Florida, eastern Cuba and the Bahamas. As of early Friday morning, the system had sustained winds of 40 miles per hour and was expected to develop a well-defined center and become Tropical Storm Alex, the first named stormed of the Atlantic Hurricane Season, according to the National Hurricane Center.

The center said the storm was likely to strengthen as it moved toward Florida on Friday, and it warned that the storm could intensify further over the weekend after it moves east of Florida and over the western Atlantic late Saturday and Sunday.

Rainfall totals associated with the storm were expected to be wide-ranging. Western Cuba could see up to 14 inches of rain with the possibility of life-threatening flash flooding and mudslides, forecasters said.

The forecast for Florida included the possibility of tornadoes over the southern portion of the state through Saturday. South Florida and the Keys could see four to eight inches of rain, with isolated totals up to 12 inches. The center warned of “considerable” flash flooding and said that some cities along the coast could see a storm surge of up to three feet.

As of early Friday morning, the storm was about 125 miles north of Cozumel, Mexico, or about 420 miles southwest of Fort Myers, Fla. It was moving northeast at six m.p.h. and was expected to continue across the southeastern Gulf of Mexico through Friday night and then across portions of Florida on Saturday.

Hurricane Agatha, the first named storm in the eastern Pacific region, roared into Mexico this week as a Category 2 storm with heavy rains and damaging winds. It killed at least 11 people and left 20 missing, The Associated Press reported.

The concern for dangerous weather in the Atlantic began this week when forecasters said a large area of disturbed weather, related to the remnants of Hurricane Agatha, had formed near the Yucatán Peninsula and had interacted with an upper-level trough over the Gulf of Mexico.