Hurricane Michael strengthened and continued its trajectory northward on Monday, tracking away from the Caribbean and toward the southeastern United States. Michael was classified as a Category 1 hurricane as of 10 a.m. Cayman time on Monday, when its maximum sustained winds were measured at 75 mph.

As the storm strengthened, the National Hurricane Center in Miami issued a hurricane warning for the Cuban province of Pinar del Rio and a tropical storm warning for the Cuban province of the Isle of Youth, as well as for the Mexican coastline ranging from Tulum to Cabo Catoche.

The NHC projects that Michael will strengthen to a major hurricane – which denotes maximum winds greater than 110 mph – before making landfall over Florida at some point on Wednesday.

The storm was about 264 miles northwest of Grand Cayman when it was classified as a hurricane. Forecasters at the Cayman Islands National Weather Service did not expect it to heavily impact Cayman.

Kerry Powery, the chief meteorologist for the Cayman Islands National Weather Service, noted Monday morning that there is a large band of scattered showers about 50 miles west of Grand Cayman. Mr. Powery said that he did not expect heavy rain locally, judging from the storm’s trajectory.

Asked the likelihood of Hurricane Michael impacting Cayman, Mr. Powery said, “That’s the $10 million question. It depends on the motion of the storm. If it moves a little more east than northward, it may post some of the banding across our area. The bands form almost a train of convection. If it comes over us, it may linger a little while.

“As it is right now [Monday morning], I think we’re on the edge of it. It should be mostly cloudy and rainy with a couple showers coming through.”

Gilbert Miller, a forecaster for the Cayman Islands National Weather Service, said that the 1 p.m. update from the National Hurricane Center indicated that the storm remained on a northward trajectory. The storm was 293 miles northwest of Grand Cayman at the time of the 1 p.m. update.

The 11 a.m. update from the National Hurricane Center indicated that hurricane-force winds extended 30 miles from the storm’s center, and tropical storm-force winds extended up to 175 miles away.

A potential storm surge of eight-to-12 feet was forecast for Florida’s western coastline from Indian Pass to Crystal River. The weather advisory warned of potential mudslides in Cuba and life-threatening flash floods for areas of Florida, the mid-Atlantic states and ranging up to southern New England.

Mr. Powery said that the Caribbean is still vulnerable to storms over the next six weeks.

“During the hurricane season, the genesis area tends to shift around,” he said. “This is getting to be our most vulnerable time of year because there are a lot of storms that generate in the western Caribbean and then track northward through western Cuba or the eastern Yucatan peninsula.”