The hurricane's maximum sustained winds Tuesday morning are near 75 mph (120 kph) with some additional strengthening possible during the day. The hurricane is expected to weaken Wednesday and Thursday.
Cosme is centered about 365 miles (585 kilometers) south of Cabo San Lucas, Mexico, and is moving northwest near 18 mph (30 kph).
The U.S. National Hurricane Center in Miami says the storm will generate large swells that will affect parts of Mexico's Pacific coast Tuesday and parts of southern Baja California starting Tuesday night and into Thursday. The swells are likely to cause dangerous surf and rip current conditions.