Hurricane-force winds of 125 miles per hour (over 200 kp/h) whipped roofs clean off buildings, ripped trees from the ground and forced evacuations along the coast.
French Prime Minister Edouard Philippe insisted that the government's support for Irma's victims isn't "empty words" and that it was "completely mobilized" to rescue and rebuild.
All 1,600 inhabitants of hurricane-ravaged Barbuda have been moved to the larger and less severely affected island of Antigua.
That was before Hurricane Jose. He said the United States has yet to pledge help. At least 20 people are known to have died so far across the Caribbean. Nonetheless the authorities warn that the effects of the extensive storm will remain for several hours.
The outer band of Irma, which has killed at least 22 people in the Caribbean, was already lashing South Florida with tropical storm-force winds and left almost 25,000 people without power, Governor Rick Scott said.
Earlier warnings for Ciego de Avila, Sancti Spiritus and Villa Clara were discontinued. Many houses have been flattened in BVI and efforts are being made to find accommodation for people made homeless. The huge storm - said to be the size of Florida - is now heading for Miami, where 5.6 million people have been told to get out immediately.More news: Did Trump Make a DACA Deal With Democrats?
Hurricane-strength winds later were recorded in the northern half of Camaguey province, the agency said.
Irma has already rampaged through a string of Caribbean islands, leaving at least 19 people dead and many injured.
The Fort Louis Marina in Marigot is seen on September 8, 2017 in Saint-Martin island, devastated by Hurricane Irma.
A Tropical Storm Watch has been issued for St. Thomas and St. John.
Castaner said many islanders had suffered "an impact of emotional shock, an impact that's extremely hard psychologically". "They didn't even go on board, they just looked to the water line around the motor home" and declared it a total loss. "I have lived through tropical storms before but nothing like this", Maybelis Viareal, 30, a receptionist at a hotel in the northern Cuban town of Remedios, told Reuters. Many residents there have been evacuated ahead of Jose.
The full damage from Irma has not yet been calculated, but the early estimates are grim: The islands of St. Martin and St. Barthelemy were about 80 percent to 90 percent destroyed; for Antigua, Barbuda and Anguilla, the figures are similar.
The hurricane left 60% of homes of St Martin, an island shared between France and the Netherlands, uninhabitable, with no electricity, gas or drinking water. Tropical storm conditions are possible Monday, according to the forecast. The states of Virginia and Alabama are also under states of emergency. "I am truly heartbroken by this news".
Puerto Rico narrowly avoided a direct hit as the eye moved northwest about 50 miles offshore, but were still lashed with rains and heavy winds.
Puerto Rico: more than 6000 residents of the U.S. territory are in shelters and many more without power.