Gustav's torrential rains triggered floods and mudslides that killed at least eight people in the Dominican Republic and 14 in Haiti, officials said.
Among the dead in Haiti were at least three people killed in a mudslide, a woman who died trying to cross a river and another person hit by a falling tree, officials said.
In the Dominican Republic, seven people from the same family were buried under mud when a hillside collapsed just north of Santo Domingo, the capital.
Energy companies in the region are concerned that oil and natural gas production in the US could dramatically decrease by up to 85 per cent as a result of potential damage from the storm.
Shell Oil Cosaid said it was evacuating about 300 nonessential workers from production platforms and Transocean Inc said it had pulled 30 workers off drilling rigs.
Gustav was projected to hit the US two days after the third anniversary of hurricane Katrina, which killed 1,500 people and caused at least $80 billion in damage, much of it in the US city of New Orleans.
Though pockets of the New Orleans are well on the way to recovery, many areas remain devastated.
Many residents still live in temporary homes, and shuttered houses still bear the black cross mark that was painted to help rescue teams looking for the dead.
Many people never returned, and the city's population is roughly half what it was before the storm.