Tropical Storm Nate has killed at least 22 people in Costa Rica, Nicaragua and Honduras before it moves north towards the US.
A state of emergency has been declared in the Central American nations, where more than 20 people are missing.
It has caused heavy rains, landslides and floods which are blocking roads, destroying bridges and damaging houses.
In Costa Rica, nearly 400,000 people are without running water and thousands are sleeping in shelters.
At least eight people have died in the storm there, while another 11 were killed when it moved north and reached Nicaragua, where as much as 15ins (38cm) of rain had been predicted to fall by the US’s National Hurricane Center.
Three people have been killed in Honduras, including two youths who drowned in a river, and several are reported missing.
Nate was expected to move off the eastern coast of Honduras at 23:00 ET (03:00 GMT) on Thursday, according to the National Hurricane Center.
Forecasters say the storm will gain strength and become a category one hurricane before it makes landfall on the southern coast of the United States on Sunday.
Residents from Florida to Texas have been told to prepare for the storm, which, if it does strike, might be the third major storm to hit the southern coast his year.
Both Texas and Florida are still recovering from the damage inflicted by Hurricane Harvey, which hit the former in August and caused “unprecedented damage”, and Hurricane Irma, which made landfall in Florida in September.
A state of emergency was declared in 29 Florida counties, and in New Orleans in Louisiana.
The mayor of the city told people who live on low-lying ground to evacuate.
“There is no need to panic,” Mitch Landrieu tweeted. “Be ready and prepare. Get a plan. Prepare to protect your personal property.”
Oil companies operating in the Gulf of Mexico says they are evacuating staff from platforms which lie along the predicted path of the storm.