In Costa Rica, nearly 400,000 people were without running water and thousands were sleeping in shelters.
At least six people have died in the storm there, while another 11 were killed when it moved north and reached Nicaragua. Three persons have been killed in Honduras and several are reported missing.
Costa Rica declared a national emergency, closing schools and government offices on Thursday and Friday. All train journeys were suspended and dozens of flights cancelled on Thursday.
It also closed national parks and several electricity plants.
Nate sparked heavy downpour in the Central American region since Wednesday, dumping up to 215 litres of rain per square meter in Costa Rica, Efe news quoted the National Meteorological Institute as saying.
The forecasters said Nate would gain strength and become a category 1 hurricane before it made landfall on the southern coast of US on Sunday.
Oil companies operating in the Gulf of Mexico said they were evacuating staff from platforms which lie along the predicted path of the storm, the BBC said.
The region was already recovering from several major hurricanes: Hurricane Harvey tore through Texas in August, and Hurricane Irma hit Florida in September. Another powerful storm, Hurricane Maria, ripped through the Caribbean in late September.