WASHINGTON – U.S. employers added 157,000 jobs in January, and hiring was much stronger at the end of 2012 than previously thought, providing reassurance that the job market held steady even as economic growth stalled.

The Labor Department report Friday showed a jump in hiring in the final two months of last year, just when the economy was sputtering and facing the threat of deep government spending cuts and tax increases from the fiscal cliff. The department revised up the estimated job gains for November from 161,000 to 247,000 and for December from 155,000 to 196,000.

The mostly encouraging jobs report included one negative sign: The unemployment rate rose to 7.9 percent from 7.8 percent in December. The rate is calculated from a survey of households, and more people in that survey said they were unemployed.