MIAMI, Florida (CNN) -- Tropical Storm Fay strengthened as it approached central Cuba early Sunday on a path that could place it near the Florida Keys by Monday, the National Hurricane Center said.
As of 5 a.m. ET Sunday, the center of Fay was about 125 miles south-southeast of Camaguey, Cuba, and about 445 miles southeast of Key West, Florida.
It was moving west-northwest at about 13 mph and was expected to turn northwest and slow slightly during the next couple of days, the hurricane center said.
According to the forecast track, Fay was expected to deal a glancing blow to eastern Cuba on Sunday, skirting the coastline of the island nation before coming ashore in western Cuba during the evening hours or early Monday.
The government of Cuba issued hurricane watches for Villa Clara, Cienfuegos, Matanzas, Camaguey, Ciego de Avila and Sancti Spiritus provinces, forecasters said. A hurricane watch means conditions are possible within the watch area, generally within 36 hours.
Officials in Florida were preparing for a possible hit from Fay. The storm is still forecast to cross the Florida Keys on Monday night, becoming a hurricane before it reaches Florida's Gulf Coast. However, because hurricane movements are erratic, long-range forecasts can vary.
Hurricane watches have been issued for the Florida Keys and portions of south Florida.
Various computer models put the storm's long-range track "up the western portion of the Florida Peninsula in a few days," while others place it farther west over the eastern Gulf of Mexico.
Fay barely clung to tropical storm status Saturday afternoon, with maximum sustained winds of near 40 mph with higher gusts, forecasters said.
Preparations were under way Saturday in Florida, where Gov. Charlie Crist said he had pre-emptively declared a state of emergency with the approach of Fay and partially activated the state emergency management office. Crist urged Floridians to ready themselves for the storm.
Shell Oil Co. said Saturday that it was evacuating 200 people from the Gulf of Mexico as Fay approached.
The U.S. naval base in Guantanamo Bay, Cuba, had seen a few rain bands connected with Fay move through on Saturday, said Navy Cmdr. Pauline Storum.
The base activated its destructive weather plan, she said, which mainly involves securing loose gear and making sure residents have what they need and personnel are in the right locations.
The storm, the sixth of the 2008 Atlantic season, formed Friday over the Dominican Republic in the Caribbean Sea.