Even though much of the overall rise reflected a 2.1 percent jump in utility output because of the hot weather, analysts said they were not pleased with the report.
The unexpected increase came as utility output surged with the return of colder weather after a mild January and February.
The Fed said utility output, which rose 6.3 percent during December's bitter cold, reversed itself in January and fell 10.7 percent.
The Federal Reserve said on Friday that the production slowdown was due to a 10.7 percent drop in utility output during an unusually cold January.
Output at factories alone increased two-tenths of 1 percent, but that was not enough to offset a 5.4 percent drop in utility output.
The gain may be deceptive, however, because analysts said much of the increase had probably occurred because of abnormally warm weather, which increased utility output.
The Fed said that the increases in automobile production and utility output accounted for three-fourths of the total June increase.
Reflecting the return to relatively normal weather, utility output jumped by 6.1 percent in March after falling by 1.2 percent in February.
With power off across broad stretches of the state, the storms also cut into the nation's industrial production, causing utility output to fall over 2 percent.
The production increase was swollen by a 4.4 percent leap in utility output after a cool August that minimized air-conditioner use.