WASHINGTON, March 11 (Reuters) - U.S. job openings increased in January and layoffs fell, offering more evidence the labor market was regaining its footing after wobbling late in 2020. Job openings, a measure of labor demand, rose to 6.9 million on the last day of January from 6.8 million in December, the Labor Department said in its monthly Job Openings and Labor Turnover Survey, or JOLTS report, on Thursday. The job openings rate increased to 4.6% from 4.5% in December. Layoffs dropped to 1.7 million from 1.8 million in December. That lowered the layoffs rate to 1.2% from 1.3% in December. But hiring fell to 5.3 million from 5.4 million in the prior month. The hiring rate dipped to 3.7% from 3.8% in December. The government reported last week that job growth surged in February. (Reporting by Lucia Mutikani Editing by Paul Simao)