Private-sector employment grew by 133,000 jobs from April to May, according to Automatic Data Processing's National Employment Report.

But analysts shot down the idea that the growth figure is powerful enough for a strong jobs recovery.

While analysts with Capital Economics said job creation grew over April's 113,000 employment growth figure, it is still well below the 200,000-plus gains posted in February and March.

"In addition, initial jobless claims edged back up to 383,000 last week, from 373,000 the week before that," Capital Economics said. "Obviously, that raises the downside risks a little for our forecast that the official figures will show that nonfarm payrolls increased by 175,000 this month (data due out tomorrow)."

In the week ending May 26, the advance figure for seasonally adjusted initial jobless claims was 383,000, an increase of 10,000 from the previous week's revised figure of 373,000, the Bureau of Labor Statistics reported. The four-week moving average was 374,500, an increase of 3,750 from the previous week's revised average of 370,750.

Of the 133,000 jobs created in April, small businesses launched 67,000 of those positions, while medium-sized businesses spawned 57,000 new jobs. Large businesses added 9,000 workers. Most jobs — 132,000 — were created in the service-producing sector. Manufacturing lost 2,000 jobs, ADP said.

Optimism was further quelched by a report from outplacement firm Challenger, Gray & Christmas, which reported that employers cut 61,887 workers from their payrolls in May, the largest cut recorded since September 2011 when 115,730 layoffs hit the economy.

The May job cuts reported by Challenger were up 53% from 40,559 planned cuts in April and up 67% from the year-ago period when 37,135 reductions were reported by the outplacement firm.

Hewlett-Packard's (HPQ) plan to cut 27,000 workers significantly contributed to May's surge in layoff reports, Challenger said. About 27,754 cuts came out of the computer industry alone.