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 shore.

Rina has maximum sustained winds of 165 km/h, 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.

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.

Mexican officials issued a hurricane warning for the east coast of the peninsula that runs from north of Punta Gruesa to Cancun. A tropical storm warning is in effect from Chetumal to Punta Gruesa.

The hurricane is centred about 480 kilometres east-southeast of Chetumal and is moving west-northwest at roughly six km/h, forecasters said Tuesday.

"A gradual turn toward the northwest with some increase in forward speed is expected over the next 48 hours," the hurricane centre said in an advisory.

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.

With files from CBC News