Forecasters at the National Hurricane Center in Miami said Sunday that Danielle had maximum sustained winds of 40 mph (65 kph) and the storm is expected to strengthen over the next couple of days.
Meanwhile, Tropical Storm Frank developed in the Pacific off Mexico, and storm warnings have been issued for parts of the coast.
Forecasters said the storm had maximum sustained winds of 50 mph (85 kph). It was about 140 miles (225 km) south-southeast of Puerto Angel, Mexico. It was moving west at 7 mph (11 kph).
Mexico has issued a tropical storm warning for the coast from Puerto Angel west to Punta Maldonado. Watches also were in effect for parts of the coast.