Gonzalo's winds were whirling at 145 miles (233 kilometres) per hour, taking it back up a notch on the five-point Saffir-Simpson scale, the US National Hurricane Center said.
It was expected to pass near Bermuda, which could see flooding along the coast. Gonzalo, which has already killed one person in the Caribbean, triggered a hurricane warning for the British overseas territory.
Bermuda Premier Michael Dunkley said government offices and schools would be closed Friday in the grouping of islands home to about 60,000 people.
At 1500 GMT, the storm was located about 485 miles south-southwest of the Bermudian archipelago. It was moving north at seven miles per hour, according to the Miami-based NHC.
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"This general motion is expected to continue today," the NHC said.
"A turn toward the north-northeast and an increase in forward speed are expected tonight and Friday."
But the forecasters stressed that major hurricanes like Gonzalo tend to fluctuate in strength.
The storm could weaken later Thursday and on Friday, but Gonzalo is on track to be a "dangerous hurricane" when it moves near Bermuda, the NHC said.
"A dangerous storm surge is expected to produce significant coastal flooding in Bermuda," the NHC said.
"Near the coast, the surge will be accompanied by large and destructive waves."
Bermuda Weather Service director Kimberley Zuill said Gonzalo would be "a long duration system" that will impact Bermuda with severe weather for about 27 straight hours, according to comments reported by The Royal Gazette newspaper in its online edition.
Three people were reported missing in the adjacent, French territory of St Martin and on the island of St Barthelemy after the storm passed, and French authorities expressed concern about four other people they were trying to contact.