The National Hurricane Center in Miami reports that Paul is 660 miles (1065 kilometers) south-southwest of the southern tip of Mexico's Baja California.
The storm has top sustained winds of 50 mph (85 kph), up from 40 mph (64 kph) only hours earlier. Forecasters say the tropical storm is moving westward at 13 mph (20 kph) and is expected to become a hurricane by late Sunday.
No coastal watches or warnings are in effect.
The storm is expected to turn to the northwest, decrease speed on Sunday, and then move northward on Monday.