Meanwhile, the National Hurricane Center in Miami said Tropical Storm Danielle had formed out of a tropical depression about 725 miles west of the southernmost Cape Verde Islands to become the season's fourth named storm.
The hurricane center said Frank was sporting sustained winds of 60 mph as it headed west at 8 mph. A turn toward the west-northwest and a gradual increase in forward speed were expected during the next couple of days. Frank will be moving parallel to the coast of southern Mexico if it stays on track, the center said.
The Mexican government issued tropical storm warnings for the country's coast from Puerto Angel west to Acapulca. A tropical storm watch was in effect from Acapulco to Tecpan de Galeana.
The Miami center said the warning means tropical storm conditions are possible in the watch area, generally within 48 hours.
Frank is expected to dump 3-6 inches of rain along the southern coastal region of Mexico with up to 10 inches possible in isolated areas.
Danielle had maximum sustained winds of 40 mph as it head northwest at 12 mph. The storm wasn't threatening any coastlines as of Sunday evening.
Forecasters said Danielle could be near hurricane intensity by late Tuesday.