A monthly gauge of online labor demand in the United States fell a touch in June and its decline slowed on a year-over-year basis, suggesting stabilization in the jobs market, a private research group said on Wednesday.

Monster Worldwide Inc , an online careers and recruiting firm, said its employment index fell to 117 in June from 118 in May. The current month's reading is 28 percent below the 163 mark a year ago.

While job openings posted online are at their lowest in nearly 2-1/2 years, there are encouraging signs that the worst of job losses might have passed, said Jesse Harriott, Monster's senior vice president.

The annual pace improved during the second quarter, suggesting some expansion in underlying employer demand for workers, Harriott said in a statement.

Online job availability rose in eight of the 20 industries Monster tracks and they also increased in 12 of 23 occupations it monitors.

Labor demand in the real estate, rental and leasing industry jumped the most in June, coinciding with signs of stabilization in the housing sector, Monster said.

By occupation, online job hirings for lawyers, police and fire-fighters jumped the most in June, it said.

The Monster Employment index is a monthly analysis based on a selection of corporate career sites and job boards. The margin of error is approximately plus or minus 1 percent.

(Reporting by Richard Leong, Editing by Chizu Nomiyama)