The Ulster Bank Northern Ireland Growth Tracker found that NI had now enjoyed three months in a row of strong output growth.
However, input cost inflation remained marked and output prices increased at the fastest pace in three months.
Sebastian Burnside, NatWest chief economist, said: “The Northern Ireland private sector completed a full quarter leading the pack in terms of output growth in September, an impressive feat for an economy that this time last year was struggling deep in contraction territory.
“Central to the rejuvenation of the private sector has been the success firms have had in securing new orders, and this continued in September, albeit with the pace of growth easing to a seven-month low.
“Companies continued to hire additional staff to try and deal with the influx of new work, but further reports from respondents of difficulties finding suitably skilled staff in the local labour market meant that backlogs of work accumulated again.”
He said efforts to upskill the workforce in NI would help firms ensure work got completed in time.
And he added that staff shortages could be leading to growing wage pressures, which were a factor behind a big rise in firms’ costs during the month.
While the overall picture was one of improvement, the experience varied across different sectors.
“Behind the generally positive story across the private sector, evidence of a two-speed economy has emerged.
“Growth continued to be driven by manufacturing and services, while the picture was much more muted in construction and retail.
“For now, the private sector seems in a good position to finish off the year with a flourish.”
Overall, the headline business activity index had increased to a four-month high of 56.0 in September from 55.7 in August. The sharp expansion was also the fastest of the 12 monitored UK regions and nations.
Manufacturing and services sectors posted the strongest increases in activity in September. Construction activity was also up, but retail recorded a decline.
There was a ninth consecutive month in new business, though the rate of growth was the weakest it had been since February.
And companies remained optimistic that output will increase over the coming year. Where a rise in activity was predicted, it was linked to increasing workloads and business expansion plans.
The pace of job creation in Northern Ireland was the sharpest of the UK nations and regions covered, with some evidence of a shortage in skilled candidates.