WASHINGTON – Job openings jumped in April to the highest level in 16 months, a sign that private employers may boost hiring in coming months.

The number of jobs advertised at the end of April rose to 3.1 million from 2.8 million in March, the Labor Department said Tuesday. That’s the most openings since December 2008.

Private employers accounted for the entire net gain. The government’s advertising for jobs decreased, despite the hiring of hundreds of thousands of census workers in May.

The department’s report, known as the Job Openings and Labor Turnover survey, or JOLTS, follows a disappointing employment report Friday that found private employers added only 41,000 jobs in May.

The unemployment rate fell to 9.7 percent from 9.9 percent in April.

The rise in job openings “makes you a little more upbeat about the labor market,” said Michael Feroli, chief U.S. economist at JPMorgan Chase.

The competition for jobs remains tough. There were 5 unemployed people, on average, for each job opening in April.

The biggest increases in available jobs were in professional and business services, leisure and hospitality and education and health services.

Government job openings fell by 36,000.

The report also found the number of people quitting jobs topped total layoffs for the third straight month. Nearly 2 million people quit their jobs in April.

An increasing number of people voluntarily leaving jobs is a sign of confidence in the employment market, economists say.