According to the Bank of Scotland's PMI report, the rate of expansion is at its highest for nine months.
The headline PMI figure of 49.9 indicated a fractional fall in combined manufacturing and services output.
But workforce levels have fallen for the sixth successive month amid what was described as "a further deterioration" of outstanding business levels.
The rise in new business was largely driven by manufacturing, which reported the largest rise for 21 months.
Graham Blair, of the Bank of Scotland, said: "Scotland's private sector will be encouraged by the quicker expansion in new business levels during May, even if the rise was at a relatively marginal pace.
"However, other areas of the economy are still struggling as job shedding persists and backlogs decline further."
The bank's report said a number of respondents attributed the decline in employment to the continued downturn in the oil and gas sector.
Price pressures were reported to have continued to grow, with a "marked" increase in input costs and only a "slight" rise in output prices.
Mr Blair added: "Firms will be looking for a further pick-up in demand for Scottish goods and services over the coming months in a hope to revive business activity."
Scotland's companies have reported a higher volume of new business for May.