Gamma's maximum sustained winds dropped to 35 miles per hour (55 km per hour), but the storm was expected to bring rain to southern Cuba, the Cayman Islands, Honduras and Nicaragua. Gamma lashed Central America on Saturday and killed at least 12 people, three of them in a plane crash on their way to a luxury jungle lodge owned by film director Francis Ford Coppola.
Nine of the dead were in Honduras, where another 14 people are missing. Over 5,000 people were evacuated on Honduras' Caribbean coast and rescue officials said more than 50,000 were cut off as bridges were damaged or destroyed, leaving several cities and towns isolated.
Experts said it would bypass Mexico's Yucatan peninsula, which is recovering from a battering by Hurricane Wilma three weeks ago. They also said it would probably would not directly hit southern Florida, where Wilma also wreaked havoc.
Slow-moving Gamma is the 24th named storm of a record-breaking Atlantic hurricane season.
Earlier in October, Hurricane Stan killed up to 2,000 people in Central America as flash floods and mudslides washed away whole villages.
Hurricane Katrina devastated New Orleans after slamming ashore on Aug. 29, killing more then 1,000 people.