The index, reflecting results of a survey taken in the first half of each month, rose from a revised 6.4 level for December to 9.4 for January.
Numbers above zero indicate growth.
The Fed said the new orders index slipped from a revised reading of 12.9 to 5.1, remaining positive but with gains slowing down. The shipments index, concurrently, rose slightly to hit 12.1 in the month from December's 11.9.
The survey indicated businesses were quicker to hire in January, but cutting hours. The index measuring the pace of hiring rose from 4.4 to 10. The average work week index slipped from 4.8 to minus 5.3.
Celebrity Families of 2014 [PHOTOS]