Tropical Storm Nate has killed at least 22 people in Costa Rica, Nicaragua and Honduras.
It caused heavy rains, landslides and floods which blocked roads, destroyed bridges and damaged houses.
In Costa Rica, nearly 400,000 people are without running water and thousands are sleeping in shelters.
The eye of the storm has since moved over the sea, heading towards Mexico and the United States, where it could become a hurricane.
At least eight people died in Costa Rica, while another 11 were killed when Nate moved north and reached Nicaragua, where as much as 15ins (38cm) of rain had been predicted to fall by the US National Hurricane Center.
Three people were killed in Honduras, including two youths who drowned in a river, and several are reported missing.
One man was killed in a mudslide in El Salvador, according to emergency services.
Oil companies have been evacuating staff from platforms in the Gulf of Mexico that lie along the predicted path of the storm.
In Costa Rica, people were trapped on a stretch of the Inter-American Highway known as the Mountain of Death, after the bus in which they were travelling got stuck between two landslides on Wednesday, according to La Nación newspaper.
There are also concerns crocodiles may be lurking around the overflowing Tárcoles river, and could appear in places where they are not normally expected.
"Please do not kill crocodiles," said officials, according to news site CRHoy.com. The advice was to avoid standing in overflowing water, to protect children and pets, and to call emergency services if one was spotted.
All train journeys were suspended in Costa Rica and dozens of flights cancelled on Thursday, when the weather worsened.
More than a dozen national parks popular with tourists have been closed as a precaution.
The storm also caused extensive damage to infrastructure in Nicaragua.
"Sometimes we think we think we can cross a river and the hardest thing to understand is that we must wait," Vice-President Rosario Murillo said on state radio.
"It's better to be late than not to get there at all."
Forecasters say the storm could 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 Nate, which, if it does strike, would be the third major storm to hit the southern coast this year.
A state of emergency has been declared in 29 Florida counties, and in New Orleans.
The city's mayor 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."