Thousands of people have moved into shelters supplied with food in Cuba and medical teams placed on alert.
The storm's centre was 360km from Cuba's western tip and moving north-northwest at 19km-an-hour, forecasters said on Saturday.
In the western province of Pinar del Rio, workers were moving recently harvested crops of tobacco to safe places.
Residents in New Orleans on Saturday were preparing for the storm as they commemorated the third anniversary of Hurricane Katrina which killed almost 1,000 people after striking New Orleans in 2005.
"We look forward to a better day, even as we prepare for a threat to come," said Ray Nagin, the mayor of New Orleans.
George Bush, the US president, has declared a state of emergency in Texas and Louisiana.
Haley Barbour, the governor of Mississippi, has called for the evacuation of residents living in trailers and other temporary housing along the state's 113km coastline, where they have been since Hurricane Katrina struck.
Gustav is also on track to strike the heavy concentration of US oil and natural gas platforms off Louisiana.
Oil prices rose in the face of Gustav's threat to the 4,000 oil facilities in the Gulf of Mexico that produce a quarter of US oil.
Energy companies evacuated offshore workers and shut production in preparation for the most serious storm since the devastating 2005 Atlantic hurricane season.
|New Orleans residents marked the anniversary of Katrina [Reuters]
The most likely route the hurricane is forecast to take has it going ashore west of New Orleans on Tuesday.
"It's too early to know exactly what kind of impact - no two storms are alike - but there's got to be concern anywhere in Louisiana perhaps even as far west as extreme east Texas and as far east as the Florida panhandle,"
Bill Read, the director of the National Hurricane Centre, told Al Jazeera.
"I'm hoping ... the preparations and actions taken will be more orderly and save more lives than we have in the past.
"Cuba is the grand target for today ... I'd say the western half of Cuba will experience impacts from the storm," Read said.
The National Hurricane Centre warned earlier that flash flooding and mudslides were possible in Cuba, where between 15cm to 30cm of rain could fall when the storm hits.
State of emergency
Forecasts predict that Gustav will strike the US coast as a category three hurricane on either Monday or Tuesday. The highest category on the Saffir-Simpson scale is a five.
Bush's declaration of a state of emergency in Louisiana empowers federal authorities to lead all disaster relief efforts "to save lives, protect property and public health and safety, or to lessen or avert the threat of a catastrophe", the White House said.
Gustav slammed into Haiti as a hurricane on Tuesday killed at least 59 people as well as eight in the neighbouring Dominican Republic and five in Jamaica.
The storm weakened before buffeting Jamaica with high winds and heavy rains.
Four people drowned and one man fell to his death when a strong gust blew him out of a tree where he was picking breadfruit, police said.