Rina was a Category 1 hurricane with maximum sustained winds of 85 mph, down from a Category 2 level with 110 mph gales in late morning, the National Hurricane Center in Miami said in its 11 p.m. EDT advisory.
The eye of the storm was about 140 miles south-southeast of Cozumel, Mexico, and about 120 miles east of Chetumal, Mexico, and was moving northwest at 6 mph. Hurricane-force winds extended 15 miles from Rina's eye and tropical storm-force winds were recorded 80 miles out.
"Preparations to protect life and property should be rushed to completion in the warning area," the forecasting center said. "Tropical storm conditions are probably already occurring in portions of the tropical storm warning area. Hurricane conditions are expected to begin within the hurricane warning area on Thursday."
The government of Belize discontinued a tropical storm watch for the coast of Belize from Belize City to the Mexican border. A hurricane watch was posted for the northeast coast of the Yucatan Peninsula from north of Punte Gruesa to San Felipe, and a tropical storm warning was in effect for the east coast of the Yucatan Peninsula from Chetumal to Punta Gruesa, and for the north coast of the peninsular west of San Felipe to Progreso.
Rina was expected to gradually turn to the north with a slight increase in forward speed Thursday. On its forecast track, Rina's center will move near or over the east coast of the Yucatan Peninsula Thursday night and Friday.
"No important changes in intensity are expected on Thursday, but a gradual weakening should begin thereafter," the center said.
The storm is expected to produce 8 to 16 inches of rain over the eastern Yucatan Peninsula and Cozumel through Friday.
A dangerous storm surge will elevate water levels by 2 to 4 feet above normal tide levels along the coast near and to the right of the center's track, forecasters said. Near the coast, the surge will be accompanied by large, destructive waves.
Authorities in tourist areas along Mexico's Caribbean coast closed ports and schools Wednesday, the Los Angeles Times reported.
Despite the downgrading of Rina to a Category 1 storm, the head of Mexico's weather service, Adrian Vazquez, told the newspaper the country has "suffered a lot with even lesser conditions, with tropical depressions and tropical storms that are supposedly lower categories and at times generate much bigger disasters."
Some flights at the Cancun airport were canceled but otherwise the airport was operating normally. Some seaports and schools were shut down and diving, snorkeling and other water activities were suspended.
More than 1,100 shelters have been set up and some evacuations were being carried out in coastal areas normally prone to storm damage, the Times said.
Residents and travelers in the popular Mexican resort city of Cancun stocked up on supplies or tried to make plans to leave before the storm hits, CNN reported.
U.S. officials issued a travel alert, advising Americans in the area to prepare for the possibility of a hurricane.
"We wanted to get out of there," Kathy Davis, an American with a timeshare in Cancun, told CNN while waiting at the airport for a flight. "We were on vacation and just didn't want to be stressed."
Kelly McLaughlin, a Canadian who has lived in Cancun for eight years, said preparing for storms is routine since Hurricane Wilma ravaged the area in 2005.
"I'm just checking everything to make sure there's nothing loose," McLaughlin said.