Dorian, now a Category 1 hurricane with winds of 75 mph and higher, is on a track for eastern Puerto Rico, according to the National Hurricane Center. More than six inches of rain was expected in some areas.
San Juan is more prepared this time around than it was in 2017 when hurricanes Irma and Maria devastated the island, according to Mayor Carmen Yulia Cruz Soto.
The Virgin Islands were being lashed with heavy rains and some flooding midday on Wednesday.
A curfew is in effect in the British Virgin Islands from 2 p.m. Wednesday until 6 a.m. Thursday, or until the all-clear is issued, according to BVI governor Augustus Jaspert.
Heavy rains are expected to reach Puerto Rico by Wednesday evening and then move out to the northwest, heading for the Bahamas by Friday or Saturday. It is expected to make landfall along Florida's southeast coast by early Sunday, when Dorian could be a Category 3 storm.
Meanwhile, the all-clear was given on Wednesday for islands earlier impacted by Dorian with heavy rain, including St. Lucia and Barbados. The French island of Martinique was hit with flash flooding but reported no heavy damage to structures, residents or visitors.
The Sustainable Tourism Conference in St. Vincent is in progress, having started a day late due to Dorian. However, Neil Walters, acting secretary general of the Caribbean Tourism Organization, the conference sponsor, was unable to make it from Barbados to St. Vincent due to the storm.
He acknowledge his regrets in a video presentation instead to delegates, saying that "this conference is very timely, given the present climatic circumstances."
Major air carriers serving the northeastern Caribbean are offering flight waivers until Dorian passes through the area.
Also, Royal Caribbean closed its private island in the Bahamas, CocoCay, until Sept. 4, and some ships have altered routes to avoid the storm.