Gustav is on a collision course with the U.S. Gulf coast and could hit Louisiana, where the governor has already declared a state of emergency. At least 22 people have died from the tropical storm.
Weather officials say Gustav is expected to pass between the southern coast of Cuba and Jamaica sometime Thursday, as travels west.
Louisiana's governor has called for 3,000 members of the National Guard to help prepare for the storm.
The storm has all ready wreaked havoc in the Caribbean.
Eight people killed by Gustav in the Dominican Republic were all members of the same family living in the capital of Santo Domingo, according to the country's civil defence agency.
More than 5,000 people in the small island nation were evacuated because of the storm.
Meanwhile, on the other side of the island in Haiti, at least three people died from the storm.
On Wednesday, tropical storm Gustav stalled in the Caribbean but meteorologists say it will soon strengthen again to hurricane status.
As of 8 p.m. ET Wednesday, Gustav's maximum sustained winds were near 75 km/h with higher wind gusts. The storm was centered about 100 kilometres south of Guantanamo, Cuba.
Forecasters say Gustav could become a Category 2 hurricane Thursday, with winds hitting 154 km/h, as it passes between Jamaica and Cuba.
"It's going to pick up to hurricane strength again," Canadian Hurricane Centre's Peter Bowyer told CTV's Canada AM on Wednesday. "There's lots of warm water out there and the conditions are just right."
Bowyer said Cuba could be hit really badly by the storm.
"The track of this is really a nasty one for Cuba because it doesn't just pass through one spot," he said. "It's tracking right on the south coast of Cuba so they could be impacted all the way."
A hurricane warning is in effect for parts of Cuba, including the U.S. military base at Guantanamo Bay.
Meanwhile, Jamaica issued a tropical storm warning Wednesday and remains under a hurricane watch. The Cayman Islands is also under a watch -- issued when hurricane conditions are possible within 36 hours.
By Sunday, Gustav is expected to enter the central gulf. Forecasters are hesitant to predict Gustav's path beyond the weekend.
Still, the price of oil jumped Tuesday after reports that Gustav could enter the gulf as a major hurricane.
A powerful storm in the region could force shutdowns on the offshore rigs in the Gulf of Mexico -- responsible for a quarter of U.S. crude production.
With files from The Associated Press
