Updated at 1:38 p.m. ET
MEXICO CITY - Mexican authorities set up emergency shelters and cruise ships shifted course on Tuesday as Hurricane Rina strengthened off the Caribbean's coast on a projected track that would carry it to Mexico's resort-dotted Caribbean coast.
Rina's maximum sustained winds have increased to 105 mph, said the U.S. National Hurricane Center in Miami, making it a Category 2 storm. Forecasters said it could strengthen as it nears the Mexican coast Wednesday night and then could roll over the Cozumel-Cancun area on Thursday.
The forecast track shows it curving east toward Cuba by the weekend, but CBS News hurricane consultant David Bernard said it could also move toward southern Florida.
After Thursday, the winds in the atmosphere will become less favorable for strengthening, and it's possible Rina will go inland, which would weaken it heading into the weekend, Bernard reports.
Yassir Espinoza, a clerk at the small Plaza Azul hotel in Cozumel, said tourists were being warned of the impending storm.
"We told them if there is a hurricane there won't be any electricity or water for at least three days."
At least eight cruise ships were changing itineraries away from the storm's path, said Carnival Cruise Lines spokesman Vance Gulliksen.
Officials in Quintana Roo state said they were readying more than 1,100 shelters that could handle nearly 200,000 people, though so far there was no word of any planned evacuations.
The hurricane was centered about 305 miles southeast of the Mayan ruins of Tulum on the Quintana Roo coast at midday Tuesday and it was and is moving west-northwest at near 3 mph, the Hurricane Center said.
Forecasters said it was likely to strengthen into a Category 3 hurricane with sustained winds of about 115 mph by night.
A Category 3 storm carries winds ranging between 111 mph and 130 mph and could generate a storm surge between 9 feet and 12 feet. By contrast, a Category 2 storm has winds measuring between 96 mph and 110 mph with an expected storm surge ranging between 6 feet and 8 feet.
The Center said the storm could produce as much as 16 inches of rain over at least parts of the eastern Yucatan Peninsula while raising water levels by as much as 5 to 7 feet in places.
The rainfall particularly worries authorities in the Gulf coast state of Tabasco, where about 300,000 people are still flooded following eight days of heavy rains.
In Central America, affected by Rina's outer bands earlier, fishermen on Monday found a Nicaraguan Navy boat that had gone missing with 29 people aboard. It had been used to evacuate an island.