Harvey, the eighth named storm of the Atlantic hurricane season, had top sustained winds of about 60 mph, up from 40 mph earlier Wednesday.
The National Hurricane Center in Miami said there was a small chance Harvey could become a hurricane — with sustained winds of at least 74 mph — when its center passes near Bermuda on Thursday morning.
A tropical storm warning was posted for Bermuda, meaning tropical storm conditions were expected within 24 hours. Two to 4 inches of rain were possible for the islands that sit about 1,000 miles northeast of Miami, meteorologists said.
At 5 p.m. EDT, the tropical storm was centered 165 miles west-southwest of Bermuda, the hurricane center said. It was moving north-northeast at about 10 mph.
Harvey is the earliest eighth named storm on record for the Atlantic hurricane season, which began June 1 and runs through Nov. 30.
The government on Tuesday sharply boosted its forecast for hurricanes this season, predicting the season total would reach 18 to 21 named storms. That was up from a forecast in May of 12 to 15 named storms.
In years that have seen at least eight named storms, the eighth storm develops, on average, on Sept. 29, said hurricane specialist James Franklin.
"In about half the years, we don't even get that far," Franklin said.