The employment component rose slightly for a second straight month to 53.2 from 52.9 in August, but it was revised downward from a 53.9 flash reading.
Earlier on Friday, the government's closely watched monthly payrolls report showed 207,000 services sector jobs created last month, accounting for more than 80 percent of the 248,000 jobs created overall.
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"A slowing in the pace of service sector growth in September matched a similar easing in the pace of manufacturing output growth seen during the month, suggesting the overall pace of economic expansion dipped to the weakest since May," said Chris Williamson, chief economist at Markit.
"But the surveys nevertheless still point to the economy growing at an annualized rate of at least 3 percent in the third quarter."
Markit's final composite PMI, a weighted average of its manufacturing and services indexes, dipped for a third straight month to 59.0 from 59.7 in August, but was up slightly from a flash reading of 58.8.