The private sector created more jobs than expected in September, but the pace slowed amid growing signs that the labor market is getting tighter, according to a report Wednesday from ADP and Moody's Analytics.

Companies hired 135,000 more workers in the month, ahead of the 125,000 that economists surveyed by Dow Jones had expected. That was a drop from the 157,000 in August, a number that itself saw a sharp downward revision from the initially reported 195,000.

September's gain was the slowest since June and brought the 2019 monthly average down to 145,000, a steep decline from the 214,000 for the same time period last year.

"We are in a very critical place, kind of a fragile juncture in the economy," Mark Zandi, chief economist at Moody's, said during a media conference call. "What happens over the next few weeks, next few months, will determine whether there's an economic downturn in 2020."

Companies with fewer than 50 employees saw the slowest hiring gain for the month at just 30,000. Large firms, with at least 500 workers, created 67,000 new jobs, while medium-sized businesses added 39,000.

In a separate interview with CNBC, Zandi pointed out that hiring toward the end of September was "meaningfully weaker" than at the beginning of the month.

"Demand for labor is beginning to weaken. Hiring is weakening across the board," he said on "Squawk Box."