The private sector added 135,000 jobs in May — an increase from 113,000 in April, but well under analyst estimates, HR staffing firm ADP said Wednesday.

In its National Employment Report, ADP said financial industry jobs represented 7,000 of the new positions. Despite these gains, jobs in financial services failed to offset weakness in construction, a sector that lost 6,000 positions.

The job growth is positive, but not strong enough to signal a strong turnaround, analysts with Econoday suggested.

"Expectations, however, were looking for a greater rate of improvement with the Econoday consensus calling for a gain 171,000 in May," staffers with the research firm said.

Additionally, Mark Zandi, chief economist for Moody’s Analytics, noted, "The job market continues to expand, but growth has slowed since the beginning of the year. The slowdown is evident across all industries and all but the largest companies. Manufacturers are reducing payrolls."

He added, "The softer job market this spring is largely due to significant fiscal drag from tax increases and government spending cuts."