Humberto is forecast to become a hurricane by Sunday night but is expected to stay offshore of Florida's eastern coast as it moves toward open waters.
The announcement from the National Hurricane Centre came after it had warned early Friday that a strengthening tropical depression was headed for the same islands hit by Dorian last week.
Bahamian meteorologists said the islands of Grand Bahama and Abaco, which were the worst-hit by Hurricane Dorian, were in the path of the approaching weather system.
Early Friday, tropical disturbances swept over the central Bahamas, packing winds of 45km/h and expected to drop 8 to 13cm of rain through Sunday.
Officials in the Bahamas believe that there are 1,300 people missing after Hurricane Dorian plowed into the islands, a sharp decline from the 2,500 listed on the missing registry a day earlier.
At least 50 people died in the hurricane which slammed into the northern Bahamas as a Category 5 storm while officials say they expect the number to rise significantly.
The death toll increased to 50 in the Bahamas, where Hurricane Dorian pummeled 320 km/h winds, according to a spokesman for the islands' National Emergency Management Agency.
NBC, citing a representative for Prime Minister Hubert Minnis, said the official count is now 43 and the number is expected to rise significantly.
Dorian lashes the Carolinas with driving rain and fierce winds after devastating the Bahamas and killing at least 30 people.
At 11:00 pm (0300 GMT Thursday), the NHC said Dorian was located 105 miles south of Charleston, South Carolina and moving north at around seven miles per hour approaching the US coast.
At least seven deaths were reported in the Bahamas. The storm's punishing winds and muddy brown floodwaters severely damaged thousands of homes, crippled hospitals and trapped people in attics.
Hurricane Dorian came to a catastrophic daylong halt over the northwest Bahamas, flooding the islands of Abaco and Grand Bahama with walls of water that lapped into the second storeys of buildings. The storm spurred evacuations in southeastern US.
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