However, the number of jobs created was the lowest for three years and was well under half the number expected by analysts.
The US had bad weather in December, which may have stalled hiring plans.
The fall in the rate, now at its lowest since October 2008, in part reflects people leaving the labor force.
The government counts people as unemployed only if they say they are actively searching for work.
The leisure, manufacturing and services sectors added jobs in December, but construction cut 16,000 jobs, the biggest drop in the industry in 20 months.
In the four months before December, the average number of jobs created in the US was 214,000 a month.
Other figures on employment have suggested a healthy jobs market, and the Labor Department said 38,000 more jobs in November were created than the 203,000 previously reported.
Overall, the US economy is picking up steam, with recent figures for consumer spending, trade and factory output all strong.
This year, economists expect the US economy to grow by 3%, well up on the 1.7% last year.
The improving picture led the Federal Reserve to start to taper its massive monetary stimulus program from $85 billion a month to $75 billion.
If the Fed remains confident about the direction of the economy, it may trim this back further at its next meeting at the end of this month.
The meeting will be the last one chaired by Ben Bernanke, who will leave the post after eight years. He will be replaced by Janet Yellen on February 1st.
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