At 8 p.m. EDT, the National Hurricane Center said Cristobal's center had moved to 25 miles south-southeast of Cape Hatteras with maximum sustained winds increasing to near 50 mph. The storm was moving to the northeast at 9 mph.
The advisory said the storm's center would head away from the coast early Monday, and predicted little change in strength over the next day or two.
The National Hurricane Center issued a tropical storm warning from Cape Lookout to the Virginia-North Carolina border, including Pamlico Sound.
Cristobal's strongest winds were east of the center, out at sea, National Weather Service meteorologist Rich Bandy said. Winds on the coastal side of the storm were about 25 mph and will have little impact on coastal cities unless the storm strengthens.
"There is a little more rain than earlier in the day," Bandy said. "It's not like the whole area is being inundated."
Bandy said some rain was falling over the smoldering wildfire that has burned 64 square miles in Pocosin Lakes National Wildlife Refuge since it was started by lightning June 1.
"We're still seeing fairly continuous bands of showers and isolated thunderstorms moving through eastern North Carolina," said Mark Willis, a meteorologist at the National Weather Service bureau in Newport. "There are going to be some areas that don't receive anything and other areas will get several inches."
The prospect of seeing Cristobal head out to sea pleased a fishing captain at Ocracoke, an island south of Cape Hatteras.
"Let's get it over with so we can go fishing," said Capt. David Nagel, who has operated the "Drum Stick" charter boat for 31 years. "Nobody's out. Everybody's tied up."
Nagel said he saw ominous clouds looming to the south and the seas outside his harbor were 6 to 8 feet with winds blowing about 25 mph.
Rainfall was expected to be 1 to 2 inches with isolated amounts of 4 to 5 inches in areas where heavy rain bands passed overhead, Bandy said.
Cristobal's winds were expected to push tides 2 to 3 feet above normal. The National Weather Service said a few areas could see flooding from heavy rain.
Minor flooding was reported Saturday in Wilmington, N.C., and the area picked up 3.43 inches of rain, a record for the day.
Dolly, the fourth named storm of the Atlantic hurricane season, sped toward the Cancun area on Sunday, packing sustained winds of 45 mph and prompting a tropical storm warning for the Yucatan peninsula.
At 5 p.m. EDT, the center of the storm was about 165 miles southeast of Cozumel, according to the U.S. National Hurricane Center.
Tropical storms have maximum sustained winds of at least 39 mph.
The Hurricane Center also said Tropical Storm Bertha had lost its tropical system characteristics and was expected to weaken during the next day or so. The center of Bertha was 850 miles east-northeast of Cape Race, Newfoundland.
The Atlantic hurricane season runs through Nov.