The storm was meandering over the far southeastern part of Louisiana early Monday, about 20 miles southeast of New Orleans, said forecaster Richard Pasch at the National Hurricane Center in Miami.
Bertha formed Sunday night in the Gulf of Mexico, causing forecasters to issue a tropical storm warning for the Mississippi and southeast Louisiana coasts. The warning was expected to end later Monday, when Bertha was forecast to weaken to a tropical depression, Pasch said.
"Bertha is barely a tropical storm," Pasch told CBS News Radio shortly before the storm was downgraded. "The maximum wind is near 40 mph … and the center's not well-defined at the moment."
The second tropical storm of the Atlantic hurricane season, Bertha should drop from 3 to 5 inches of rain on Monday across parts of southern Mississippi and southeast Louisiana, Pasch said. Isolated areas could receive up to 8 inches, he added.
"August and September are the peak of the hurricane season," said meteorologist Dan Brown at the National Hurricane Center. "This is kind of a wake-up call.
"Make sure you have all the hurricane supplies ready, just in case something bigger comes along."
New Orleans is particularly vulnerable. A major hurricane could put the city under 15 feet of water.
Southern Alabama and parts of the Florida Panhandle were likely to have less rainfall. However, those areas were under a coastal flood watch early Monday.
Bertha's maximum sustained winds were near 40 mph earlier Monday, barely past the 39 mph threshold for it to be considered a tropical storm.
The storm should continue moving over southern Louisiana until early Tuesday, Pasch said.
The Atlantic hurricane season runs from June 1 to Nov. 30.