By later today, it may become Tropical Storm Maria, and in advance of that, tropical storm watches have been issued for parts of the Windward and Leeward Islands, including St. Lucia, Martinique, Guadeloupe and Dominica.
The hurricane was forecast to pass east of the North Carolina coast Monday and stay offshore from Virginia to New England.
It's still too early to tell whether Lee or Maria will have any direct impact on the Lowcountry. The islands of Antigua, Barbuda, St. Kitts, Nevis, and Montserrat issued hurricane watches Saturday.
As of 5 p.m., the storm was 620 miles away from the Lesser Antilles.
"On the forecast track, the center of Jose will move over the western Atlantic Ocean between the east coast of the United States and Bermuda through Monday". The storm is moving toward the Caribbean at 19 miles per hour, according to the National Hurricane Center.
Vázquez said forecasters measured wind gusts of up to 114 miles per hour in the small island of Culebra during Hurricane Irma, which didn't directly hit Puerto Rico. If Jose grows stronger or makes landfall, more significant effects are likely including property damage, widespread power outages and flooding rainfall.
Wind shear continues to limit growth of Jose, but forecasters say the warm water it is rising over is keeping the storm at hurricane strength.
The peninsular region that's home to the twin resort cities of Cabo San Lucas and San Jose del Cabo was hit about two weeks ago by Tropical Storm Lidia, which flooded streets and homes and killed at least four people.
Long-range models suggest that the strengthening high-pressure area will then force the hurricane to move west-northwest toward the East Coast, according to the Weather Underground.
By Monday night, the leading edge of rain bands could reach southern New England, but most weather models bring the bulk of the rain showers into far southeastern New England by early Tuesday with the gusty onshore winds by Tuesday afternoon and continuing into Wednesday.