The Bureau of Labor Statistics said the hires rate -- the number of hires as a percentage of the total employment -- was also little changed at 3.3 percent, while the separations rate remained 3.2 percent.
While the total number of jobs was little changed, jobs did shift in the month, rising in retail trades and dropping in professional and business services.
In the Midwest, the number of job openings rose, but the three other regions saw the number stagnant in the month, the bureau said.
Similarly, job openings remained little changed in May from May 2012, but there was a shift that included increased opportunities in retail, transportation, warehousing and utilities and finance and insurance. This was offset by declines in professional and business services and in manufacturing jobs involving durable goods.