Its maximum sustained winds were blowing at 40 mph (65 kph) as Oscar moved north-northeast at 9 mph (14 kph). The storm early Tuesday was about 70 miles (115 kilometers) south of Long Island, Bahamas, the U.S. National Hurricane Center in Miami said. A tropical storm warning was in effect for the central and southeastern Bahamas.
Oscar is the smallest hurricane on record, with a wind field of only about 6 miles (10 kilometers) across, according to hurricane specialist and storm surge expert Michael Lowry.
He noted that not a single forecast model indicated that Oscar might strengthen into a hurricane on Saturday before making landfall in the Bahamas. "It's not often we see a colossal failure in hurricane forecasting," he wrote in an analysis published Monday.
Oscar was a Category 1 hurricane with winds of 75 mph (120 kph) when it made landfall in the eastern Cuban province of Guantanamo, near the city of Baracoa, on Sunday evening.
RELATED: Hurricane Oscar causes at least 6 deaths in Cuba amid days-long power outage
Flooding in low-lying areas was reported and at least six deaths. Cubans were already suffering from a major power outage that has knocked out power and water across the island since last week.
Oscar earlier made landfall on Saturday on Great Inagua in the Bahamas, where residents were evacuated after their homes were damaged.
Meanwhile, Tropical Storm Kristy formed off Mexico's southern Pacific coast Monday. The storm was 315 miles (510 kilometers) southwest of Acapulco and was moving west at 16 mph (26 kph). It had sustained winds of 45 mph (75 kph), according to the National Hurricane Center.
Kristy was forecast to strengthen into a hurricane Wednesday but continue moving over open waters without threatening land.