WASHINGTON (Reuters) - Job openings were harder to come by in April as private sector hiring ebbed, further evidence that the labor market remains precarious, Labor Department data showed on Tuesday.

There were 2.97 million open positions in April, down from 3.12 million in March, according to the government's Job Openings and Labor Turnover Survey (JOLTS). The hiring rate dipped slightly to 3.0 percent from 3.1 percent.

Private sector hires slipped to 3.71 million from 3.81 million, and the rate eased to 3.4 percent from 3.5 percent.

The level of total hires has risen from a trough of 3.6 million in October of 2009, but remains well below the 5.0 million leveled that prevailed before the economy entered a prolonged recession, at the end of 2007.

The report comes just as data last week showed the economy added a disappointing 54,000 new jobs in May and the unemployment rate rose to 9.1 percent, sparking worries the recovery might be faltering.

The JOLTS figures encompass employment data from about 16,000 establishments across the country.

(Reporting by Pedro Nicolaci da Costa, Editing by Chizu Nomiyama)

(This story is corrected to show April and March figures in paragraph 2)