Maximum sustained winds from Nate, the fourth major storm to hit the United States in less than two months, dropped to 35 miles per hour (55 km per hour) as it moved through Alabama and into Tennessee.
The remnants of the storm spawned tornado warnings in those states and the western portions of North Carolina and South Carolina. It is forecast to bring gusty winds and up to 4 inches (10 cm) of rain to parts of Ohio, Pennsylvania and New York on Monday.
The storm made landfall as a Category 1 hurricane, the weakest designation by the U.S. National Hurricane Center. Only a few hours earlier, its winds had been blowing at 70 mph (113 kph) but appeared to lack the devastating punch of its recent predecessors.
Mississippi Governor Phil Bryant told reporters there had been no deaths or reports of catastrophic damage. "We are very fortunate this morning and have been blessed," he said.
Nate killed at least 30 people in Central America before entering the warm waters of the Gulf of Mexico and bearing down on the U.S. South. It has also shut down most oil and gas production in the Gulf.
Nate follows hurricanes Harvey, Irma and Maria, which have devastated areas of the Caribbean and southern United States.
The tropical depression's center will move up through Alabama into Tennessee and Kentucky through Monday, the hurricane center said. Heavy rainfall and storm-surge flooding remained a danger across the region, and the hurricane center said Florida's Panhandle and parts of Alabama and Georgia might feel tropical storm-force wind gusts.
Nate made its first U.S. landfall on Saturday evening near the mouth of the Mississippi River and then made a second one early on Sunday near Biloxi, Mississippi.
In Biloxi, water surged over roads during the storm and quickly receded on Sunday, leaving a boat that broke loose marooned on the beach. At a Waffle House restaurant, the storm surge deposited a dumpster in its parking lot.