While some wind shear is preventing the storm from explosively intensifying, Nate is expected to strengthen right up until landfall.
Just hours earlier, Nate had made its first USA landfall near the mouth of the Mississippi River in southeast Louisiana, with winds of 85 mph the National Hurricane Center reported Saturday night.
The storm's centre will move inland over MS and across the deep south, Tennessee Valley and Central Appalachian Mountains through Monday, the National Hurricane Centre said.
Tropical-storm-force wind gusts are expected over the the Florida Panhandle, and portions of Alabama and Georgia through on Sunday, the NHC said.
Louisiana, Mississippi, Alabama and parts of Florida have issued hurricane warnings and evacuation orders.
The storm doused Central America with heavy rains on Thursday, killing at least 12 people in Nicaragua, nine in Costa Rica, two in Honduras and two in El Salvador, local authorities said.
State officials said at a briefing Friday in Gulfport that Nate's main dangers will be a potential for 10 feet (3 meters) of storm-surge in low-lying areas and high winds that could damage mobile homes.
The hurricane center says conditions are favorable for Nate to continue strengthening as it crosses the Gulf.
Nate was downgraded from a hurricane to a tropical storm early on Sunday and was expected to weaken as it moved further inland, the National Hurricane Centre said.
"This is the worst hurricane that has impacted Mississippi since Hurricane Katrina", Mississippi Emergency Management Director Lee Smithson said on Saturday.
Edwards thanked Trump for approving Louisiana's predisaster emergency declaration for 17 south Louisiana parishes. It's now a Category 1 hurricane with 90 miles per hour winds steadily increasing.
Those who live in the Gulf Coast states are bracing for Hurricane Nate. He announced 1,300 National Guard troops are being mobilized and 15 are heading to New Orleans to monitor the pumping system.
Tornadoes could form beginning late Saturday afternoon over parts of the central Gulf Coast, the hurricane center said. But Gov. Carlos Joaquin said it appeared the storm would stay well offshore and not hit land, adding "that, I believe, is good news".
"It kind of surprised us", Mike Kovacevich, who lives two blocks north of USA 90, told Biloxi officials on their Facebook page.
Tropical Storm Nate roared toward Mexico's Yucatan Peninsula Friday after drenching Central America in rain that was blamed for at least 22 deaths, and forecasters said it could reach the U.S. Gulf Coast as a hurricane over the weekend. Oil company workers have been evacuated from 301 platforms and 13 rigs as of Saturday, the BSEE said.
Drillers including BP Plc and Chevron Corp. evacuated and shut oil and gas platforms in the Gulf.
In Alabama, the Port of Mobile closed Saturday, meaning the Carnival Fantasy cruise ship would not be "making its scheduled call" there Sunday, the Mobile Alabama Cruise Terminal said.