The storm, with maximum sustained winds of 85mph, made landfall near the mouth of the Mississippi River in Louisiana on October 7.
Moving north, Nate made a second landfall at Biloxi, Mississippi.
Louisiana, Mississippi, Alabama and parts of Florida earlier issued warnings and evacuation orders amid fears of rapidly rising sea waters.
Tropical Storm Nate killed at least 25 people in Nicaragua, Costa Rica and Honduras.
It then strengthened to a category one hurricane on the Saffir-Simpson scale as it headed towards the US.
Although not as strong as last month’s Maria and Irma, officials had warned Nate was a fast-moving storm that could bring flooding to low-lying areas.
On October 7, President Donald Trump issued an emergency declaration for Louisiana, allowing the state to seek federal help with preparation and possible relief efforts.
In Alabama, Republican Governor Kay Ivey urged residents in areas facing heavy winds and storm surges to take precautions.
Five ports along the Gulf Coast were closed to shipping as a precaution.
Most oil and gas platforms in the US Gulf of Mexico evacuated their staff and stopped production ahead of the storm.
In an update at 03:00 GMT, the NHC said a hurricane warning was in effect for the “mouth of the Pearl River to the Alabama-Florida border”.
Evacuation orders were put in place for some low-lying areas.
Louisiana Governor John Bel Edwards declared a state of emergency ahead of the hurricane, saying more than 1,000 National Guard troops had been mobilized with a number sent to New Orleans to monitor the drainage pumps there.
A mandatory curfew from 18:00 local time was in place in New Orleans, where residents from areas outside the city’s levee system were evacuated.
A tropical storm warning is currently in effect for New Orleans.
The NHC said that Hurricane Nate “is expected to weaken quickly after landfall, and it is likely to become a tropical storm on October 8.
“It should degenerate into a remnant low late Monday.”
Nate went past Mexico’s Yucatan Peninsula – home to the popular beach resorts of Cancun and Playa del Carmen – on Friday night as it headed north, the NHC said.
Nate caused heavy rains, landslides and floods which blocked roads, destroyed bridges and damaged houses as it tore through central America.
At least 13 people died in Nicaragua, eight in Costa Rica, three in Honduras and one in El Salvador.
The tail of the storm is still causing problems in the region, where thousands have been forced to sleep in shelters and some 400,000 people in Costa Rica were reported to be without running water.
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