WASHINGTON — U.S. employers advertised more job openings in January, suggesting that hiring will remain healthy in coming months.

Job openings rose 2.2 percent in January from December to 3.69 million, the Labor Department said Tuesday. Openings had fallen nearly 5 percent in December, and they remain below November’s level of 3.8 million.

Yet the report provided further evidence that the U.S. job market is strengthening. Employers laid off the fewest workers in January than in any month since records began in 2001. And the number of Americans who quit their jobs rose to the highest in more than four years. People usually quit when they have another job, so more quitting suggests it is easier to find work.

The biggest increase in job openings was in professional and business services, which includes high-paying fields such as accounting, engineering, and architecture. It also includes temp jobs, which typically carry few benefits. The next-largest gain was in retail.

On Friday, the government reported that hiring in February was robust: Employers added 236,000 jobs, and the unemployment rate fell to a four-year low of 7.7 percent from 7.9 percent in January. February capped a fourth-month hiring spree in which employers added an average of 205,000 jobs a month.

At the same time, the competition for open positions remains strong. About 12.3 million people were unemployed in January, which means there were 3.3 unemployed people, on average, competing for each job. That’s sharply down from a peak of nearly 7 unemployed people competing for each job in July 2009. In a healthy economy, the ratio is roughly 2 to 1.

The report, known as the Job Openings and Labor Turnover survey, or JOLTS, calculates total hiring, layoffs and quits. By contrast, the department’s monthly jobs report measures the unemployment rate and net hiring. Net hiring equals total hiring minus layoffs, quits and other separations.