Nate, which currently has 85 kilometre per hour winds, is forecast to reach hurricane strength by the time it makes landfall in the United States tomorrow, on the north coast of the Gulf of Mexico.
New Orleans, where levees were breached during Hurricane Katrina in 2005, and other cities on the US Gulf coast were under hurricane watch.
The US National Hurricane Centre warned of possible "hurricane conditions" by tonight on Mexico's Yucatan Peninsula, home to Cancun and other Caribbean resorts.
"Nate is expected to become a hurricane by the time it reaches the northern Gulf of Mexico," the Centre said.
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As of this afternoon, the storm was located about 125 kilometres east of Cozumel, Mexico, a picturesque resort island.
It was still wreaking havoc in Central America, where Honduran officials ordered several coastal zones to evacuate as heavy rains continued causing floods.
Authorities in Honduras, Guatemala and El Salvador declared a maximum or red alert.
Yesterday, intense rains from the storm forced thousands from their homes, uprooted trees, knocked out bridges and turned roads into rivers in Costa Rica, Nicaragua and Honduras.
Nicaragua bore 12 of the deaths, according to Vice President Rosario Murillo.
In Costa Rica, where a national emergency was declared, nine people died, including a three-year-old girl, after they were hit by falling trees and mudslides. An alert was issued for people to be wary of crocodiles that might be roaming after rivers and estuaries flooded.
Three other people were killed in Honduras, and two in El Salvador.
Nicaragua's Murillo said 800 people had been evacuated, nearly 600 homes were flooded and 14 communities were isolated because of rains that had been falling for days.
More than 5,000 people were staying in shelters in Costa Rica after having to abandon their homes because of flooding and the risk of mudslides.
In the Gulf of Mexico, some offshore oil and gas rigs were evacuated ahead of the storm's advance, the US government Bureau of Safety and Environmental Enforcement said in a statement.