With 1,300 people still missing, according to the Bahamian government, relief services are focused on search and rescue as well as providing food, water and shelter.
The announcement from the NHC came after it had warned early Friday that a strengthening tropical depression was heading for the same islands hit by Dorian last week.
While the official death toll is at 50, the number is "expected to significantly increase" as around 1,300 people are still reported missing.
Al Jazeera's Alan Fisher reports from the capital, Nassau.
Dexter Wilson, a 40-year-old maintenance man who was helping a friend put a blue tarp on a damaged roof in Grand Bahama under a bright sun, said he was anxious about his brother in Abaco given the tropical storm.
He said storms powered by climate change had grown more intense, and he implored the worldwide community to learn from the example of Abaco and Grand Bahama and provide support.
It equalled the highest winds ever recorded for a hurricane at landfall when it struck the Abaco Islands.
The storm, dubbed Humberto, is expected to strengthen into a hurricane, moving very near the northwestern Bahamas on Saturday, before shifting to offshore Florida after the weekend, the Miami-based forecaster said.
"And I don't make wild statements", he said.
The hurricane centre said most of the heavy squalls were occurring north and east of the centre of the storm, which was passing just east of Abaco. Until a low-level center forms for the storm, forecast models will struggle with it, he said. The Bahamian government discontinued a tropical storm warning earlier in the evening.
The storm could delay the movement of food and water already on the ground, said Carl Smith, spokesman for the National Emergency Management Agency.
Dave McGregor, president and COO of the Grand Bahama Power Company, said crews would resume restoring power as soon as possible.
On Wednesday (Sept 11), the health minister for the Bahamas, Mr Duane Sands, said teams of dog handlers from the US, Canada and Belgium are uncovering more and more dead bodies among the debris.
The tropical cyclone was not expected to bring anywhere near that level of devastation.
"We have always had many hurricanes, but now they are more intense, and they are more frequent", he said.