Centered about 425 miles (685 km) west of Bermuda, Cristobal was moving north at 12 miles per hour (19 km per hour) with maximum sustained winds of 80 mph (130 kph), the NHC said. It is seen turning northeast with a gradual increase in forward speed over the next two days.
"Cristobal has a large wind field. Hurricane force winds extend outward up to 60 miles (95 km) from the center and tropical storm force winds extend outward up to 205 miles (335 km)," the hurricane center said in an advisory.
The hurricane is expected to produce an additional one to two inches (2.5 to five cm) of rain over Bermuda, and some strengthening of its winds was possible during the next day or so, the NHC added.
The NHC said swells generated by the hurricane were affecting Bermuda and parts of the U.S. coastline from North Carolina to the mid-Atlantic states. It said they would spread north to southern New England on Thursday, and were "likely to cause life-threatening surf and rip current conditions."
Cristobal, a Category 1 storm on the five-step Saffir-Simpson scale, is the third named storm of this year's Atlantic hurricane season. It soaked parts of the Bahamas and Turks and Caicos Islands earlier this week, after drenching Haiti, the Dominican Republic and Puerto Rico last weekend.
Forecasters this month downgraded their outlook for the 2014 Atlantic hurricane season, predicting below-normal activity with seven to 12 named storms, with no more than two reaching major hurricane status. A major hurricane is considered to be Category 3 or above with winds hitting at least 111 mph (178 kph).
Separately, the NHC said on Wednesday that shower and thunderstorm activity associated with a weak low pressure area over the northwestern Gulf of Mexico had increased during the past few hours.
Some additional development was possible before the system moves inland over south Texas and northern Mexico on Thursday, it said, adding that a U.S. Air Force Hurricane Hunter aircraft was scheduled to investigate the system on Wednesday if needed.
It also said a tropical wave several hundred miles east of the Lesser Antilles was producing "disorganized cloudiness and showers," and it said that system is expected to move westward across the Caribbean Sea during the next few days.
"Environmental conditions could become favorable for some development by early next week in the western Caribbean Sea or southern Gulf of Mexico," the NHC said. (Reporting by Daniel Wallis; Editing by Eric Beech)