"It could have been worse," Avila said. "They were very, very lucky."
Omar knocked down trees, caused some flooding and minor mudslides but there were no immediate reports of deaths or major damage in the U.S. Virgin Islands, said Mark Walters, director of the disaster management agency for the Caribbean territory.
A last-minute shift to the east spared St. Croix, the most populated of the islands.
The nearby British Virgin Islands also emerged largely unscathed, said Deputy Gov. Inez Archibald, noting there was little damage beyond some mudslides and scattered debris.
"We did reasonably well actually," Inez told The Associated Press. "We did not get what we expected."
The island's international airport reopened Thursday afternoon, but the Virgin Gorda airport remained closed because of flooding.
Omar began weakening as it headed over the ocean. By late Thursday morning, it was centered about 180 miles (290 kilometers) northeast of the northern Leeward Islands and moving northeast about 23 mph (37 kmh). It had maximum winds of 85 mph (140 kph).
Omar was taking an unusual southwest-to-the-northeast track toward the central North Atlantic, well away from the U.S. mainland.
On Thursday, cleanup crews fanned out across several flooded Caribbean islands, where power and water were slowly being restored.
Ports in Puerto Rico reopened, but remained closed in St. Croix.
In St. Maarten, roads were flooded and littered with tree branches and other debris, but authorities lifted a curfew Thursday afternoon and planned to reopen the main airport on Friday.
Lt. Gov. Franklyn Richards urged people to go to church and give thanks for being spared.
In Dominica, Prime Minister Roosevelt Skerrit toured the island's west coast.
"There is substantial damage to housing, fishing boats and port infrastructure," he said.
On the Puerto Rican island of Vieques, which was brushed by the storm, people returned home from shelters where they spent the night and awaited the resumption of ferry service to the mainland of the U.S. island territory.
"Everything was calm, nothing happened," said Joselyn Ponce of the local office of emergency services.
One death was reported on Puerto Rico's tiny island of Culebra. Authorities say a 55-year-old man collapsed from cardiac arrest while trying to install storm shutters on his house.
The island's Hovensa oil refinery, one of the 10 largest in the world, shut down operations for the storm.
Hurricane Omar forced at least three cruise ships to change course and flights were canceled on several islands.