The average had hit a five-year low earlier this month.
Only one state, Kansas, reported layoffs above 1,000, with 2,344 layoffs.
Still, there were 157,000 jobs added in January and job gains during the end of the year were larger than previously estimated, which is positive news for millions of workers struggling to get back into the labor force
In January, the economy added 157,000 jobs, and employers added more jobs than initially estimated in November and December.
Some economists expect that unemployment rate will gradually drop to 7 percent by the end of the year before falling below 7 percent in 2014.
The economy contracted during the final three months of the year on a sharp drop in defense spending. But economists are expecting substantial revisions that will probably show that the economy is growing, though at an anemic rate.