"Rina has the potential to become a major hurricane today or tonight," the U.S. National Hurricane Center said.
Rina is a Category Two hurricane on the Saffir-Simpson intensity scale, packing winds of 110 mph. When sustained winds hit 111 miles per hour storms are considered major Category Three hurricanes.
The sixth hurricane in the Atlantic season this year, Rina was located 215 miles east southeast of Chetumal, Mexico, and 235 miles south southeast of Cozumel early on Wednesday, and was moving west at 5 mph (7 km/h).
The storm was expected to be near or over the east coast of the Yucatan peninsula late Wednesday and on Thursday.
Some cruise ships revised their travel schedules and the governor of Quintana Roo ordered hundreds of people evacuate the fishing village of Punta Allen on the Yucatan peninsula's western coast on Tuesday night.
DOLPHINS MOVED INLAND
On Tuesday, authorities in the city of Cancun were preparing 50 shelters ahead of Rina, while worried residents stocked up on gas and cleared out store shelves of emergency supplies like water and canned tuna in case businesses decide to shut down.
On Tuesday there were around 80,000 tourists in the state of Quintana Roo, mostly foreigners at big hotels in Cancun.
Companies that run marine parks around Cancun moved more than two dozen dolphins, some of them pregnant, housed in areas in the hurricane's path to safer sites further inland.
The hurricane could dump 8 to 16 inches of rain over the eastern Yucatan peninsula from Wednesday morning. "Preparations to protect life and property should be rushed to completion," the hurricane center said.
A huge storm surge is also possible, raising tide level as much as 7 feet above normal along the coast.
The storm could slam into other tourist hubs like Playa del Carmen and the island of Cozumel, popular with scuba divers and cruise ships, and will also graze the small Central American nation of Belize.
Belize issued a tropical storm watch along its coastline north of Belize City.
Carnival reportedly revised eight cruise itineraries to avoid the hurricane and Norwegian Cruise Line put out an alert on its website saying it was closely monitoring Rina's path.
All the ports in the Gulf of Mexico remained open on Tuesday. Most of Mexico's major oil installations are further east in the Gulf of Mexico, far from the hurricane's path.
El Salvador and the United Nations launched an appeal for $15.7 million to help 300,000 people affected by the floods.
In Guatemala, the situation was similarly grave, with a half million people hit by flooding and 50 percent of the country's roads blocked by landslides or overflowing rivers.
(Writing by Mica Rosenberg in Mexico City; Editing by Jackie Frank)