The National Hurricane Center in Miami said Sunday morning that Debby was about 170 miles (270 km) southeast of the mouth of the Mississippi River. It said the storm warning has now been issued from the Mississippi-Alabama border eastward to the Florida Panhandle's Ochlockonee River.
Debby's top sustained winds had increased to about 60 mph (95 kph). The storm was crawling along toward the north at 2 mph (4 kph).
Although a forecast track was still uncertain, the hurricane center said people from Texas to Florida should remain alert to Debby's movement.
At least one tornado linked to the storm touched down Saturday in southwest Florida, but no injuries were reported. Heavy squalls pounded parts of that state.