Rainfall associated with the tropical storm will begin to diminish today across southern Texas. It will continue to impact large regions of Central America.
The rain will likely produce flash flooding. Mudslides are also possible in some areas.
Moderate coastal flooding is likely among much of the Texas coast through the morning.
In the Mexican state of Nuevo Leon, civil protection authorities reported three deaths linked to Alberto's rains.
They said one man died in the La Silla river in the city of Monterrey, the state capital, and that two minors died from electric shocks in the municipality of Allende. Local media reported that the minors were riding a bicycle in the rain.
More tropical activity
Another tropical system is developing in the western Atlantic Ocean, near the Bahamas. This system has a low chance to develop into a named storm. However, forecasters continue to monitor it as it moves west northwest toward the southeastern United States.
The area of showers and storms is currently located several hundred miles east of the Bahamas. It's expected to arrive on the US coast by the end of the week.
The National Oceanic and Atmospheric Administration predicts the hurricane season that began June 1 and runs through Nov. 30 is likely to be well above average, with between 17 and 25 named storms. The forecast calls 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.
A no-name storm earlier in June dumped more than 20 inches (50 centimeters) of rain on parts of South Florida, stranding numerous motorists on flooded streets and pushing water into some homes in low-lying areas.
Difference between hurricanes, tropical storms and tropical depressions
Once a depression sustains wind over 39 mph, it is called a tropical storm.
If a storm develops strong rotation, and the wind speeds exceed 74 mph, we have a hurricane. Hurricanes are classified from categories 1 to 5.
The Associated Press contributed to this report.