He urged everyone in Dorian’s path to obey warnings and evacuation orders issued by local authorities, saying public safety “must always come first”.
Mr Trump approved an emergency declaration for Florida on Friday.
The announcement came as the Category 4 storm unleashed massive flooding across the Bahamas, shredding roofs, hurling cars and forcing even rescue crews to take shelter.
In the US, the National Hurricane Centre extended watches and warnings across the Florida and Georgia coasts. Forecasters expect Dorian to stay just off shore, but meteorologist Daniel Brown cautioned that “only a small deviation” could draw the storm’s dangerous core toward land.
By Monday afternoon, the storm’s top sustained winds fell slightly to 150mph, and it was crawling along Grand Bahama Island at just 1mph.
On Sunday, Dorian’s maximum sustained winds reached 185mph with gusts up to 220mph, tying the record for the most powerful Atlantic hurricane to make landfall.
That equalled the Labour Day hurricane of 1935, before storms were named. The only recorded storm that was more powerful was Hurricane Allen in 1980, with 190mph winds, although it did not make landfall at that strength.
Forecasters said Dorian is likely to begin pulling away from the Bahamas early on Tuesday and curving to the north east parallel to the south-eastern coast of the US.